-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_transformed_target.html
535 lines (472 loc) · 61.9 KB
/
plot_transformed_target.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
<!DOCTYPE html>
<!-- data-theme below is forced to be "light" but should be changed if we use pydata-theme-sphinx in the future -->
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" data-content_root="../../" data-theme="light"> <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" data-content_root="../../" data-theme="light"> <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="Effect of transforming the targets in regression model" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/compose/plot_transformed_target.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="In this example, we give an overview of TransformedTargetRegressor. We use two examples to illustrate the benefit of transforming the targets before learning a linear regression model. The first ex..." />
<meta property="og:image" content="https://scikit-learn.org/stable/_static/scikit-learn-logo-small.png" />
<meta property="og:image:alt" content="scikit-learn" />
<meta name="description" content="In this example, we give an overview of TransformedTargetRegressor. We use two examples to illustrate the benefit of transforming the targets before learning a linear regression model. The first ex..." />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Effect of transforming the targets in regression model — scikit-learn 1.4.1 documentation</title>
<link rel="canonical" href="http://scikit-learn.org/stable/auto_examples/compose/plot_transformed_target.html" />
<link rel="shortcut icon" href="../../_static/favicon.ico"/>
<link rel="stylesheet" href="../../_static/css/vendor/bootstrap.min.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/copybutton.css" type="text/css" />
<link rel="stylesheet" href="../../_static/plot_directive.css" type="text/css" />
<link rel="stylesheet" href="../../https://fonts.googleapis.com/css?family=Vibur" type="text/css" />
<link rel="stylesheet" href="../../_static/jupyterlite_sphinx.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-binder.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-dataframe.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sg_gallery-rendered-html.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/js/vendor/jquery-3.6.3.slim.min.js"></script>
<script src="../../_static/js/details-permalink.js"></script>
</head>
<body>
<nav id="navbar" class="sk-docs-navbar navbar navbar-expand-md navbar-light bg-light py-0">
<div class="container-fluid sk-docs-container px-0">
<a class="navbar-brand py-0" href="../../index.html">
<img
class="sk-brand-img"
src="../../_static/scikit-learn-logo-small.png"
alt="logo"/>
</a>
<button
id="sk-navbar-toggler"
class="navbar-toggler"
type="button"
data-toggle="collapse"
data-target="#navbarSupportedContent"
aria-controls="navbarSupportedContent"
aria-expanded="false"
aria-label="Toggle navigation"
>
<span class="navbar-toggler-icon"></span>
</button>
<div class="sk-navbar-collapse collapse navbar-collapse" id="navbarSupportedContent">
<ul class="navbar-nav mr-auto">
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../install.html">Install</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../user_guide.html">User Guide</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../../modules/classes.html">API</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" href="../index.html">Examples</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link" target="_blank" rel="noopener noreferrer" href="https://blog.scikit-learn.org/">Community</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../getting_started.html" >Getting Started</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../tutorial/index.html" >Tutorial</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../whats_new/v1.4.html" >What's new</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../glossary.html" >Glossary</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../faq.html" >FAQ</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../support.html" >Support</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../related_projects.html" >Related packages</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../roadmap.html" >Roadmap</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../governance.html" >Governance</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="../../about.html" >About us</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
</li>
<li class="nav-item">
<a class="sk-nav-link nav-link nav-more-item-mobile-items" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</li>
<li class="nav-item dropdown nav-more-item-dropdown">
<a class="sk-nav-link nav-link dropdown-toggle" href="#" id="navbarDropdown" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">More</a>
<div class="dropdown-menu" aria-labelledby="navbarDropdown">
<a class="sk-nav-dropdown-item dropdown-item" href="../../getting_started.html" >Getting Started</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../tutorial/index.html" >Tutorial</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../whats_new/v1.4.html" >What's new</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../glossary.html" >Glossary</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/developers/index.html" target="_blank" rel="noopener noreferrer">Development</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../faq.html" >FAQ</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../support.html" >Support</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../related_projects.html" >Related packages</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../roadmap.html" >Roadmap</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../governance.html" >Governance</a>
<a class="sk-nav-dropdown-item dropdown-item" href="../../about.html" >About us</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://github.com/scikit-learn/scikit-learn" >GitHub</a>
<a class="sk-nav-dropdown-item dropdown-item" href="https://scikit-learn.org/dev/versions.html" >Other Versions and Download</a>
</div>
</li>
</ul>
<div id="searchbox" role="search">
<div class="searchformwrapper">
<form class="search" action="../../search.html" method="get">
<input class="sk-search-text-input" type="text" name="q" aria-labelledby="searchlabel" />
<input class="sk-search-text-btn" type="submit" value="Go" />
</form>
</div>
</div>
</div>
</div>
</nav>
<div class="d-flex" id="sk-doc-wrapper">
<input type="checkbox" name="sk-toggle-checkbox" id="sk-toggle-checkbox">
<label id="sk-sidemenu-toggle" class="sk-btn-toggle-toc btn sk-btn-primary" for="sk-toggle-checkbox">Toggle Menu</label>
<div id="sk-sidebar-wrapper" class="border-right">
<div class="sk-sidebar-toc-wrapper">
<div class="btn-group w-100 mb-2" role="group" aria-label="rellinks">
<a href="plot_feature_union.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Concatenating multiple feature extraction methods">Prev</a><a href="index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Pipelines and composite estimators">Up</a>
<a href="plot_digits_pipe.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Pipelining: chaining a PCA and a logistic regression">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.4.1</strong><br/>
<a href="http://scikit-learn.org/dev/versions.html">Other versions</a>
</p>
</div>
<div class="alert alert-warning p-1 mb-2" role="alert">
<p class="text-center mb-0">
Please <a class="font-weight-bold" href="../../about.html#citing-scikit-learn"><string>cite us</string></a> if you use the software.
</p>
</div>
<div class="sk-sidebar-toc">
<ul>
<li><a class="reference internal" href="#">Effect of transforming the targets in regression model</a><ul>
<li><a class="reference internal" href="#synthetic-example">Synthetic example</a></li>
<li><a class="reference internal" href="#real-world-data-set">Real-world data set</a></li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div id="sk-page-content-wrapper">
<div class="sk-page-content container-fluid body px-md-3" role="main">
<div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-compose-plot-transformed-target-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="effect-of-transforming-the-targets-in-regression-model">
<span id="sphx-glr-auto-examples-compose-plot-transformed-target-py"></span><h1>Effect of transforming the targets in regression model<a class="headerlink" href="#effect-of-transforming-the-targets-in-regression-model" title="Link to this heading">¶</a></h1>
<p>In this example, we give an overview of
<a class="reference internal" href="../../modules/generated/sklearn.compose.TransformedTargetRegressor.html#sklearn.compose.TransformedTargetRegressor" title="sklearn.compose.TransformedTargetRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">TransformedTargetRegressor</span></code></a>. We use two examples
to illustrate the benefit of transforming the targets before learning a linear
regression model. The first example uses synthetic data while the second
example is based on the Ames housing data set.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Guillaume Lemaitre <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
</pre></div>
</div>
<section id="synthetic-example">
<h2>Synthetic example<a class="headerlink" href="#synthetic-example" title="Link to this heading">¶</a></h2>
<blockquote>
<div><p>A synthetic random regression dataset is generated. The targets <code class="docutils literal notranslate"><span class="pre">y</span></code> are
modified by:</p>
<blockquote>
<div><ol class="arabic simple">
<li><p>translating all targets such that all entries are
non-negative (by adding the absolute value of the lowest <code class="docutils literal notranslate"><span class="pre">y</span></code>) and</p></li>
<li><p>applying an exponential function to obtain non-linear
targets which cannot be fitted using a simple linear model.</p></li>
</ol>
</div></blockquote>
<p>Therefore, a logarithmic (<code class="docutils literal notranslate"><span class="pre">np.log1p</span></code>) and an exponential function
(<code class="docutils literal notranslate"><span class="pre">np.expm1</span></code>) will be used to transform the targets before training a linear
regression model and using it for prediction.</p>
</div></blockquote>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_regression.html#sklearn.datasets.make_regression" title="sklearn.datasets.make_regression" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_regression</span></a>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_regression.html#sklearn.datasets.make_regression" title="sklearn.datasets.make_regression" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_regression</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">10_000</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.expm1.html#numpy.expm1" title="numpy.expm1" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">expm1</span></a><span class="p">((</span><span class="n">y</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">min</span><span class="p">()))</span> <span class="o">/</span> <span class="mi">200</span><span class="p">)</span>
<span class="n">y_trans</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.log1p.html#numpy.log1p" title="numpy.log1p" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">log1p</span></a><span class="p">(</span><span class="n">y</span><span class="p">)</span>
</pre></div>
</div>
<p>Below we plot the probability density functions of the target
before and after applying the logarithmic functions.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a>
<span class="n">f</span><span class="p">,</span> <span class="p">(</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2000</span><span class="p">])</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Probability"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Target"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Target distribution"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">y_trans</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Probability"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Target"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Transformed target distribution"</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">"Synthetic data"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1.05</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_transformed_target_001.png" srcset="../../_images/sphx_glr_plot_transformed_target_001.png" alt="Synthetic data, Target distribution, Transformed target distribution" class = "sphx-glr-single-img"/><p>At first, a linear model will be applied on the original targets. Due to the
non-linearity, the model trained will not be precise during
prediction. Subsequently, a logarithmic function is used to linearize the
targets, allowing better prediction even with a similar linear model as
reported by the median absolute error (MedAE).</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.median_absolute_error.html#sklearn.metrics.median_absolute_error" title="sklearn.metrics.median_absolute_error" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">median_absolute_error</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">r2_score</span></a>
<span class="k">def</span> <span class="nf">compute_score</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">):</span>
<span class="k">return</span> <span class="p">{</span>
<span class="s2">"R2"</span><span class="p">:</span> <span class="sa">f</span><span class="s2">"</span><span class="si">{</span><a href="../../modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score" title="sklearn.metrics.r2_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">r2_score</span></a><span class="p">(</span><span class="n">y_true</span><span class="p">,</span><span class="w"> </span><span class="n">y_pred</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span>
<span class="s2">"MedAE"</span><span class="p">:</span> <span class="sa">f</span><span class="s2">"</span><span class="si">{</span><a href="../../modules/generated/sklearn.metrics.median_absolute_error.html#sklearn.metrics.median_absolute_error" title="sklearn.metrics.median_absolute_error" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">median_absolute_error</span></a><span class="p">(</span><span class="n">y_true</span><span class="p">,</span><span class="w"> </span><span class="n">y_pred</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span>
<span class="p">}</span>
</pre></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.compose</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.compose.TransformedTargetRegressor.html#sklearn.compose.TransformedTargetRegressor" title="sklearn.compose.TransformedTargetRegressor" class="sphx-glr-backref-module-sklearn-compose sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TransformedTargetRegressor</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RidgeCV</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">PredictionErrorDisplay</span>
<span class="n">f</span><span class="p">,</span> <span class="p">(</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ridge_cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RidgeCV</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_ridge</span> <span class="o">=</span> <span class="n">ridge_cv</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">ridge_cv_with_trans_target</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.compose.TransformedTargetRegressor.html#sklearn.compose.TransformedTargetRegressor" title="sklearn.compose.TransformedTargetRegressor" class="sphx-glr-backref-module-sklearn-compose sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TransformedTargetRegressor</span></a><span class="p">(</span>
<span class="n">regressor</span><span class="o">=</span><a href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RidgeCV</span></a><span class="p">(),</span> <span class="n">func</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.log1p.html#numpy.log1p" title="numpy.log1p" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">log1p</span></a><span class="p">,</span> <span class="n">inverse_func</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.expm1.html#numpy.expm1" title="numpy.expm1" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">expm1</span></a>
<span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_ridge_with_trans_target</span> <span class="o">=</span> <span class="n">ridge_cv_with_trans_target</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"actual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax0</span><span class="p">,</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge_with_trans_target</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"actual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">,</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<span class="c1"># Add the score in the legend of each axis</span>
<span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">y_pred</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">([</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">],</span> <span class="p">[</span><span class="n">y_pred_ridge</span><span class="p">,</span> <span class="n">y_pred_ridge_with_trans_target</span><span class="p">]):</span>
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">score</span> <span class="ow">in</span> <span class="n">compute_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">([],</span> <span class="p">[],</span> <span class="s2">" "</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s2">=</span><span class="si">{</span><span class="n">score</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"upper left"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> without target transformation"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> with target transformation"</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">"Synthetic data"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1.05</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_transformed_target_002.png" srcset="../../_images/sphx_glr_plot_transformed_target_002.png" alt="Synthetic data, Ridge regression without target transformation, Ridge regression with target transformation" class = "sphx-glr-single-img"/></section>
<section id="real-world-data-set">
<h2>Real-world data set<a class="headerlink" href="#real-world-data-set" title="Link to this heading">¶</a></h2>
<blockquote>
<div><p>In a similar manner, the Ames housing data set is used to show the impact
of transforming the targets before learning a model. In this example, the
target to be predicted is the selling price of each house.</p>
</div></blockquote>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.quantile_transform.html#sklearn.preprocessing.quantile_transform" title="sklearn.preprocessing.quantile_transform" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-function"><span class="n">quantile_transform</span></a>
<span class="n">ames</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_openml.html#sklearn.datasets.fetch_openml" title="sklearn.datasets.fetch_openml" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_openml</span></a><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s2">"house_prices"</span><span class="p">,</span> <span class="n">as_frame</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Keep only numeric columns</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">ames</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">select_dtypes</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.number" title="numpy.number" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">number</span></a><span class="p">)</span>
<span class="c1"># Remove columns with NaN or Inf values</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s2">"LotFrontage"</span><span class="p">,</span> <span class="s2">"GarageYrBlt"</span><span class="p">,</span> <span class="s2">"MasVnrArea"</span><span class="p">])</span>
<span class="c1"># Let the price be in k$</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">ames</span><span class="o">.</span><span class="n">target</span> <span class="o">/</span> <span class="mi">1000</span>
<span class="n">y_trans</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.quantile_transform.html#sklearn.preprocessing.quantile_transform" title="sklearn.preprocessing.quantile_transform" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-function"><span class="n">quantile_transform</span></a><span class="p">(</span>
<span class="n">y</span><span class="o">.</span><span class="n">to_frame</span><span class="p">(),</span> <span class="n">n_quantiles</span><span class="o">=</span><span class="mi">900</span><span class="p">,</span> <span class="n">output_distribution</span><span class="o">=</span><span class="s2">"normal"</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
</pre></div>
</div>
<p>A <a class="reference internal" href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="sklearn.preprocessing.QuantileTransformer"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuantileTransformer</span></code></a> is used to normalize
the target distribution before applying a
<a class="reference internal" href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV"><code class="xref py py-class docutils literal notranslate"><span class="pre">RidgeCV</span></code></a> model.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">f</span><span class="p">,</span> <span class="p">(</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Probability"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Target"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Target distribution"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">y_trans</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Probability"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Target"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Transformed target distribution"</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">"Ames housing data: selling price"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1.05</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_transformed_target_003.png" srcset="../../_images/sphx_glr_plot_transformed_target_003.png" alt="Ames housing data: selling price, Target distribution, Transformed target distribution" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<p>The effect of the transformer is weaker than on the synthetic data. However,
the transformation results in an increase in <span class="math notranslate nohighlight">\(R^2\)</span> and large decrease
of the MedAE. The residual plot (predicted target - true target vs predicted
target) without target transformation takes on a curved, ‘reverse smile’
shape due to residual values that vary depending on the value of predicted
target. With target transformation, the shape is more linear indicating
better model fit.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="sklearn.preprocessing.QuantileTransformer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">QuantileTransformer</span></a>
<span class="n">f</span><span class="p">,</span> <span class="p">(</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><span class="s2">"row"</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">6.5</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">ridge_cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RidgeCV</span></a><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_ridge</span> <span class="o">=</span> <span class="n">ridge_cv</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">ridge_cv_with_trans_target</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.compose.TransformedTargetRegressor.html#sklearn.compose.TransformedTargetRegressor" title="sklearn.compose.TransformedTargetRegressor" class="sphx-glr-backref-module-sklearn-compose sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TransformedTargetRegressor</span></a><span class="p">(</span>
<span class="n">regressor</span><span class="o">=</span><a href="../../modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV" title="sklearn.linear_model.RidgeCV" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RidgeCV</span></a><span class="p">(),</span>
<span class="n">transformer</span><span class="o">=</span><a href="../../modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer" title="sklearn.preprocessing.QuantileTransformer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">QuantileTransformer</span></a><span class="p">(</span><span class="n">n_quantiles</span><span class="o">=</span><span class="mi">900</span><span class="p">,</span> <span class="n">output_distribution</span><span class="o">=</span><span class="s2">"normal"</span><span class="p">),</span>
<span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_pred_ridge_with_trans_target</span> <span class="o">=</span> <span class="n">ridge_cv_with_trans_target</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># plot the actual vs predicted values</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"actual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge_with_trans_target</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"actual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax0</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<span class="c1"># Add the score in the legend of each axis</span>
<span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">y_pred</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">([</span><span class="n">ax0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ax0</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span> <span class="p">[</span><span class="n">y_pred_ridge</span><span class="p">,</span> <span class="n">y_pred_ridge_with_trans_target</span><span class="p">]):</span>
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">score</span> <span class="ow">in</span> <span class="n">compute_score</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">([],</span> <span class="p">[],</span> <span class="s2">" "</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s2">=</span><span class="si">{</span><span class="n">score</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"upper left"</span><span class="p">)</span>
<span class="n">ax0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> without target transformation"</span><span class="p">)</span>
<span class="n">ax0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> with target transformation"</span><span class="p">)</span>
<span class="c1"># plot the residuals vs the predicted values</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"residual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
<span class="n">y_test</span><span class="p">,</span>
<span class="n">y_pred_ridge_with_trans_target</span><span class="p">,</span>
<span class="n">kind</span><span class="o">=</span><span class="s2">"residual_vs_predicted"</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">scatter_kwargs</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="mf">0.5</span><span class="p">},</span>
<span class="p">)</span>
<span class="n">ax1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> without target transformation"</span><span class="p">)</span>
<span class="n">ax1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Ridge regression </span><span class="se">\n</span><span class="s2"> with target transformation"</span><span class="p">)</span>
<span class="n">f</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">"Ames housing data: selling price"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mf">1.05</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_transformed_target_004.png" srcset="../../_images/sphx_glr_plot_transformed_target_004.png" alt="Ames housing data: selling price, Ridge regression without target transformation, Ridge regression with target transformation, Ridge regression without target transformation, Ridge regression with target transformation" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 1.328 seconds)</p>
<div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-compose-plot-transformed-target-py">
<div class="binder-badge docutils container">
<a class="reference external image-reference" href="https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.4.X?urlpath=lab/tree/notebooks/auto_examples/compose/plot_transformed_target.ipynb"><img alt="Launch binder" src="../../_images/binder_badge_logo5.svg" width="150px" /></a>
</div>
<div class="lite-badge docutils container">
<a class="reference external image-reference" href="../../lite/lab/?path=auto_examples/compose/plot_transformed_target.ipynb"><img alt="Launch JupyterLite" src="../../_images/jupyterlite_badge_logo5.svg" width="150px" /></a>
</div>
<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/ea57d7ab1588de8f5bd1afc68f20de2f/plot_transformed_target.ipynb"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Jupyter</span> <span class="pre">notebook:</span> <span class="pre">plot_transformed_target.ipynb</span></code></a></p>
</div>
<div class="sphx-glr-download sphx-glr-download-python docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/93d55b9dcb06fda6f82b4d16c9a3a70d/plot_transformed_target.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_transformed_target.py</span></code></a></p>
</div>
</div>
<p class="rubric">Related examples</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="An illustration of the isotonic regression on generated data (non-linear monotonic trend with h..."><img alt="" src="../../_images/sphx_glr_plot_isotonic_regression_thumb.png" />
<p><a class="reference internal" href="../miscellaneous/plot_isotonic_regression.html#sphx-glr-auto-examples-miscellaneous-plot-isotonic-regression-py"><span class="std std-ref">Isotonic Regression</span></a></p>
<div class="sphx-glr-thumbnail-title">Isotonic Regression</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The PCA does an unsupervised dimensionality reduction, while the logistic regression does the p..."><img alt="" src="../../_images/sphx_glr_plot_digits_pipe_thumb.png" />
<p><a class="reference internal" href="plot_digits_pipe.html#sphx-glr-auto-examples-compose-plot-digits-pipe-py"><span class="std std-ref">Pipelining: chaining a PCA and a logistic regression</span></a></p>
<div class="sphx-glr-thumbnail-title">Pipelining: chaining a PCA and a logistic regression</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Stacking refers to a method to blend estimators. In this strategy, some estimators are individu..."><img alt="" src="../../_images/sphx_glr_plot_stack_predictors_thumb.png" />
<p><a class="reference internal" href="../ensemble/plot_stack_predictors.html#sphx-glr-auto-examples-ensemble-plot-stack-predictors-py"><span class="std std-ref">Combine predictors using stacking</span></a></p>
<div class="sphx-glr-thumbnail-title">Combine predictors using stacking</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example shows how to use cross_val_predict together with PredictionErrorDisplay to visuali..."><img alt="" src="../../_images/sphx_glr_plot_cv_predict_thumb.png" />
<p><a class="reference internal" href="../model_selection/plot_cv_predict.html#sphx-glr-auto-examples-model-selection-plot-cv-predict-py"><span class="std std-ref">Plotting Cross-Validated Predictions</span></a></p>
<div class="sphx-glr-thumbnail-title">Plotting Cross-Validated Predictions</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The example compares prediction result of linear regression (linear model) and decision tree (t..."><img alt="" src="../../_images/sphx_glr_plot_discretization_thumb.png" />
<p><a class="reference internal" href="../preprocessing/plot_discretization.html#sphx-glr-auto-examples-preprocessing-plot-discretization-py"><span class="std std-ref">Using KBinsDiscretizer to discretize continuous features</span></a></p>
<div class="sphx-glr-thumbnail-title">Using KBinsDiscretizer to discretize continuous features</div>
</div></div><p class="sphx-glr-signature"><a class="reference external" href="https://sphinx-gallery.github.io">Gallery generated by Sphinx-Gallery</a></p>
</section>
</section>
</div>
<div class="container">
<footer class="sk-content-footer">
© 2007 - 2024, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/compose/plot_transformed_target.rst.txt" rel="nofollow">Show this page source</a>
</footer>
</div>
</div>
</div>
<script src="../../_static/js/vendor/bootstrap.min.js"></script>
<script>
window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)};ga.l=+new Date;
ga('create', 'UA-22606712-2', 'auto');
ga('set', 'anonymizeIp', true);
ga('send', 'pageview');
</script>
<script async src='https://www.google-analytics.com/analytics.js'></script>
<script defer data-domain="scikit-learn.org" src="https://views.scientific-python.org/js/script.js">
</script>
<script src="../../_static/clipboard.min.js"></script>
<script src="../../_static/copybutton.js"></script>
<script>
$(document).ready(function() {
/* Add a [>>>] button on the top-right corner of code samples to hide
* the >>> and ... prompts and the output and thus make the code
* copyable. */
var div = $('.highlight-python .highlight,' +
'.highlight-python3 .highlight,' +
'.highlight-pycon .highlight,' +
'.highlight-default .highlight')
var pre = div.find('pre');
// get the styles from the current theme
pre.parent().parent().css('position', 'relative');
// create and add the button to all the code blocks that contain >>>
div.each(function(index) {
var jthis = $(this);
// tracebacks (.gt) contain bare text elements that need to be
// wrapped in a span to work with .nextUntil() (see later)
jthis.find('pre:has(.gt)').contents().filter(function() {
return ((this.nodeType == 3) && (this.data.trim().length > 0));
}).wrap('<span>');
});
/*** Add permalink buttons next to glossary terms ***/
$('dl.glossary > dt[id]').append(function() {
return ('<a class="headerlink" href="#' +
this.getAttribute('id') +
'" title="Permalink to this term">¶</a>');
});
});
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<script src="https://scikit-learn.org/versionwarning.js"></script>
</body>
</html>