-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathplot_kernel_ridge_regression.html
521 lines (465 loc) · 57.2 KB
/
plot_kernel_ridge_regression.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
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
<meta property="og:title" content="Comparison of kernel ridge regression and SVR" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/miscellaneous/plot_kernel_ridge_regression.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="Both kernel ridge regression (KRR) and SVR learn a non-linear function by employing the kernel trick, i.e., they learn a linear function in the space induced by the respective kernel which correspo..." />
<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="Both kernel ridge regression (KRR) and SVR learn a non-linear function by employing the kernel trick, i.e., they learn a linear function in the space induced by the respective kernel which correspo..." />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Comparison of kernel ridge regression and SVR — scikit-learn 1.2.2 documentation</title>
<link rel="canonical" href="http://scikit-learn.org/stable/auto_examples/miscellaneous/plot_kernel_ridge_regression.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/plot_directive.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>
</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/v1.2.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/v1.2.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_anomaly_comparison.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Comparing anomaly detection algorithms for outlier detection on toy datasets">Prev</a><a href="index.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Miscellaneous">Up</a>
<a href="plot_pipeline_display.html" role="button" class="btn sk-btn-rellink py-1" sk-rellink-tooltip="Displaying Pipelines">Next</a>
</div>
<div class="alert alert-danger p-1 mb-2" role="alert">
<p class="text-center mb-0">
<strong>scikit-learn 1.2.2</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="#">Comparison of kernel ridge regression and SVR</a><ul>
<li><a class="reference internal" href="#generate-sample-data">Generate sample data</a></li>
<li><a class="reference internal" href="#construct-the-kernel-based-regression-models">Construct the kernel-based regression models</a></li>
<li><a class="reference internal" href="#compare-times-of-svr-and-kernel-ridge-regression">Compare times of SVR and Kernel Ridge Regression</a></li>
<li><a class="reference internal" href="#look-at-the-results">Look at the results</a></li>
<li><a class="reference internal" href="#visualize-training-and-prediction-times">Visualize training and prediction times</a></li>
<li><a class="reference internal" href="#visualize-the-learning-curves">Visualize the learning curves</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>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-miscellaneous-plot-kernel-ridge-regression-py"><span class="std std-ref">here</span></a>
to download the full example code or to run this example in your browser via Binder</p>
</div>
<section class="sphx-glr-example-title" id="comparison-of-kernel-ridge-regression-and-svr">
<span id="sphx-glr-auto-examples-miscellaneous-plot-kernel-ridge-regression-py"></span><h1>Comparison of kernel ridge regression and SVR<a class="headerlink" href="#comparison-of-kernel-ridge-regression-and-svr" title="Permalink to this heading">¶</a></h1>
<p>Both kernel ridge regression (KRR) and SVR learn a non-linear function by
employing the kernel trick, i.e., they learn a linear function in the space
induced by the respective kernel which corresponds to a non-linear function in
the original space. They differ in the loss functions (ridge versus
epsilon-insensitive loss). In contrast to SVR, fitting a KRR can be done in
closed-form and is typically faster for medium-sized datasets. On the other
hand, the learned model is non-sparse and thus slower than SVR at
prediction-time.</p>
<p>This example illustrates both methods on an artificial dataset, which
consists of a sinusoidal target function and strong noise added to every fifth
datapoint.</p>
<p>Authors: Jan Hendrik Metzen <<a class="reference external" href="mailto:jhm%40informatik.uni-bremen.de">jhm<span>@</span>informatik<span>.</span>uni-bremen<span>.</span>de</a>>
License: BSD 3 clause</p>
<section id="generate-sample-data">
<h2>Generate sample data<a class="headerlink" href="#generate-sample-data" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default 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="n">rng</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="c1"># Add noise to targets</span>
<span class="n">y</span><span class="p">[::</span><span class="mi">5</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">(</span><span class="mf">0.5</span> <span class="o">-</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">//</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">X_plot</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">100000</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span>
</pre></div>
</div>
</section>
<section id="construct-the-kernel-based-regression-models">
<h2>Construct the kernel-based regression models<a class="headerlink" href="#construct-the-kernel-based-regression-models" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="sklearn.svm.SVR" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVR</span></a>
<span class="kn">from</span> <span class="nn">sklearn.kernel_ridge</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="sklearn.kernel_ridge.KernelRidge" class="sphx-glr-backref-module-sklearn-kernel_ridge sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelRidge</span></a>
<span class="n">train_size</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">svr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="sklearn.svm.SVR" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s2">"C"</span><span class="p">:</span> <span class="p">[</span><span class="mf">1e0</span><span class="p">,</span> <span class="mf">1e1</span><span class="p">,</span> <span class="mf">1e2</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">],</span> <span class="s2">"gamma"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)},</span>
<span class="p">)</span>
<span class="n">kr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="sklearn.kernel_ridge.KernelRidge" class="sphx-glr-backref-module-sklearn-kernel_ridge sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="p">[</span><span class="mf">1e0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">1e-2</span><span class="p">,</span> <span class="mf">1e-3</span><span class="p">],</span> <span class="s2">"gamma"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)},</span>
<span class="p">)</span>
</pre></div>
</div>
</section>
<section id="compare-times-of-svr-and-kernel-ridge-regression">
<h2>Compare times of SVR and Kernel Ridge Regression<a class="headerlink" href="#compare-times-of-svr-and-kernel-ridge-regression" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">time</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">svr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_size</span><span class="p">])</span>
<span class="n">svr_fit</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Best SVR with params: </span><span class="si">{</span><span class="n">svr</span><span class="o">.</span><span class="n">best_params_</span><span class="si">}</span><span class="s2"> and R2 score: </span><span class="si">{</span><span class="n">svr</span><span class="o">.</span><span class="n">best_score_</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"SVR complexity and bandwidth selected and model fitted in </span><span class="si">%.3f</span><span class="s2"> s"</span> <span class="o">%</span> <span class="n">svr_fit</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">kr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_size</span><span class="p">])</span>
<span class="n">kr_fit</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Best KRR with params: </span><span class="si">{</span><span class="n">kr</span><span class="o">.</span><span class="n">best_params_</span><span class="si">}</span><span class="s2"> and R2 score: </span><span class="si">{</span><span class="n">kr</span><span class="o">.</span><span class="n">best_score_</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"KRR complexity and bandwidth selected and model fitted in </span><span class="si">%.3f</span><span class="s2"> s"</span> <span class="o">%</span> <span class="n">kr_fit</span><span class="p">)</span>
<span class="n">sv_ratio</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">best_estimator_</span><span class="o">.</span><span class="n">support_</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">train_size</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Support vector ratio: </span><span class="si">%.3f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">sv_ratio</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">y_svr</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">)</span>
<span class="n">svr_predict</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"SVR prediction for </span><span class="si">%d</span><span class="s2"> inputs in </span><span class="si">%.3f</span><span class="s2"> s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">X_plot</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">svr_predict</span><span class="p">))</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">y_kr</span> <span class="o">=</span> <span class="n">kr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">)</span>
<span class="n">kr_predict</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"KRR prediction for </span><span class="si">%d</span><span class="s2"> inputs in </span><span class="si">%.3f</span><span class="s2"> s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">X_plot</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">kr_predict</span><span class="p">))</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Best SVR with params: {'C': 1.0, 'gamma': 0.09999999999999999} and R2 score: 0.737
SVR complexity and bandwidth selected and model fitted in 0.519 s
Best KRR with params: {'alpha': 0.1, 'gamma': 0.09999999999999999} and R2 score: 0.723
KRR complexity and bandwidth selected and model fitted in 0.158 s
Support vector ratio: 0.340
SVR prediction for 100000 inputs in 0.118 s
KRR prediction for 100000 inputs in 0.073 s
</pre></div>
</div>
</section>
<section id="look-at-the-results">
<h2>Look at the results<a class="headerlink" href="#look-at-the-results" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default 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="n">sv_ind</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">best_estimator_</span><span class="o">.</span><span class="n">support_</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">scatter</span></a><span class="p">(</span>
<span class="n">X</span><span class="p">[</span><span class="n">sv_ind</span><span class="p">],</span>
<span class="n">y</span><span class="p">[</span><span class="n">sv_ind</span><span class="p">],</span>
<span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"SVR support vectors"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">edgecolors</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">scatter</span></a><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"data"</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span>
<span class="n">X_plot</span><span class="p">,</span>
<span class="n">y_svr</span><span class="p">,</span>
<span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"SVR (fit: </span><span class="si">%.3f</span><span class="s2">s, predict: </span><span class="si">%.3f</span><span class="s2">s)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">svr_fit</span><span class="p">,</span> <span class="n">svr_predict</span><span class="p">),</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span>
<span class="n">X_plot</span><span class="p">,</span> <span class="n">y_kr</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">"g"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"KRR (fit: </span><span class="si">%.3f</span><span class="s2">s, predict: </span><span class="si">%.3f</span><span class="s2">s)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">kr_fit</span><span class="p">,</span> <span class="n">kr_predict</span><span class="p">)</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" 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">xlabel</span></a><span class="p">(</span><span class="s2">"data"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" 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">ylabel</span></a><span class="p">(</span><span class="s2">"target"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="s2">"SVR versus Kernel Ridge"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend" 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">legend</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_kernel_ridge_regression_001.png" srcset="../../_images/sphx_glr_plot_kernel_ridge_regression_001.png" alt="SVR versus Kernel Ridge" class = "sphx-glr-single-img"/><p>The previous figure compares the learned model of KRR and SVR when both
complexity/regularization and bandwidth of the RBF kernel are optimized using
grid-search. The learned functions are very similar; however, fitting KRR is
approximatively 3-4 times faster than fitting SVR (both with grid-search).</p>
<p>Prediction of 100000 target values could be in theory approximately three
times faster with SVR since it has learned a sparse model using only
approximately 1/3 of the training datapoints as support vectors. However, in
practice, this is not necessarily the case because of implementation details
in the way the kernel function is computed for each model that can make the
KRR model as fast or even faster despite computing more arithmetic
operations.</p>
</section>
<section id="visualize-training-and-prediction-times">
<h2>Visualize training and prediction times<a class="headerlink" href="#visualize-training-and-prediction-times" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" 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">figure</span></a><span class="p">()</span>
<span class="n">sizes</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">3.8</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">estimator</span> <span class="ow">in</span> <span class="p">{</span>
<span class="s2">"KRR"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="sklearn.kernel_ridge.KernelRidge" class="sphx-glr-backref-module-sklearn-kernel_ridge sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">10</span><span class="p">),</span>
<span class="s2">"SVR"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="sklearn.svm.SVR" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e2</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">10</span><span class="p">),</span>
<span class="p">}</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">train_time</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">test_time</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">train_test_size</span> <span class="ow">in</span> <span class="n">sizes</span><span class="p">:</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_test_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_test_size</span><span class="p">])</span>
<span class="n">train_time</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
<span class="n">estimator</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">[:</span><span class="mi">1000</span><span class="p">])</span>
<span class="n">test_time</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span>
<span class="n">sizes</span><span class="p">,</span>
<span class="n">train_time</span><span class="p">,</span>
<span class="s2">"o-"</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"r"</span> <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"SVR"</span> <span class="k">else</span> <span class="s2">"g"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> (train)"</span> <span class="o">%</span> <span class="n">name</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" 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">plot</span></a><span class="p">(</span>
<span class="n">sizes</span><span class="p">,</span>
<span class="n">test_time</span><span class="p">,</span>
<span class="s2">"o--"</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"r"</span> <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"SVR"</span> <span class="k">else</span> <span class="s2">"g"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> (test)"</span> <span class="o">%</span> <span class="n">name</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xscale.html#matplotlib.pyplot.xscale" title="matplotlib.pyplot.xscale" 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">xscale</span></a><span class="p">(</span><span class="s2">"log"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yscale.html#matplotlib.pyplot.yscale" title="matplotlib.pyplot.yscale" 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">yscale</span></a><span class="p">(</span><span class="s2">"log"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" 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">xlabel</span></a><span class="p">(</span><span class="s2">"Train size"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" 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">ylabel</span></a><span class="p">(</span><span class="s2">"Time (seconds)"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="s2">"Execution Time"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend" 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">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_kernel_ridge_regression_002.png" srcset="../../_images/sphx_glr_plot_kernel_ridge_regression_002.png" alt="Execution Time" class = "sphx-glr-single-img"/><p>This figure compares the time for fitting and prediction of KRR and SVR for
different sizes of the training set. Fitting KRR is faster than SVR for
medium-sized training sets (less than a few thousand samples); however, for
larger training sets SVR scales better. With regard to prediction time, SVR
should be faster than KRR for all sizes of the training set because of the
learned sparse solution, however this is not necessarily the case in practice
because of implementation details. Note that the degree of sparsity and thus
the prediction time depends on the parameters epsilon and C of the SVR.</p>
</section>
<section id="visualize-the-learning-curves">
<h2>Visualize the learning curves<a class="headerlink" href="#visualize-the-learning-curves" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">LearningCurveDisplay</span>
<span class="n">_</span><span class="p">,</span> <span class="n">ax</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="n">svr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="sklearn.svm.SVR" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">kr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="sklearn.kernel_ridge.KernelRidge" class="sphx-glr-backref-module-sklearn-kernel_ridge sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">common_params</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"X"</span><span class="p">:</span> <span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span>
<span class="s2">"y"</span><span class="p">:</span> <span class="n">y</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span>
<span class="s2">"train_sizes"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span>
<span class="s2">"scoring"</span><span class="p">:</span> <span class="s2">"neg_mean_squared_error"</span><span class="p">,</span>
<span class="s2">"negate_score"</span><span class="p">:</span> <span class="kc">True</span><span class="p">,</span>
<span class="s2">"score_name"</span><span class="p">:</span> <span class="s2">"Mean Squared Error"</span><span class="p">,</span>
<span class="s2">"std_display_style"</span><span class="p">:</span> <span class="kc">None</span><span class="p">,</span>
<span class="s2">"ax"</span><span class="p">:</span> <span class="n">ax</span><span class="p">,</span>
<span class="p">}</span>
<a href="../../modules/generated/sklearn.model_selection.LearningCurveDisplay.html#sklearn.model_selection.LearningCurveDisplay.from_estimator" title="sklearn.model_selection.LearningCurveDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-model_selection-LearningCurveDisplay sphx-glr-backref-type-py-method"><span class="n">LearningCurveDisplay</span><span class="o">.</span><span class="n">from_estimator</span></a><span class="p">(</span><span class="n">svr</span><span class="p">,</span> <span class="o">**</span><span class="n">common_params</span><span class="p">)</span>
<a href="../../modules/generated/sklearn.model_selection.LearningCurveDisplay.html#sklearn.model_selection.LearningCurveDisplay.from_estimator" title="sklearn.model_selection.LearningCurveDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-model_selection-LearningCurveDisplay sphx-glr-backref-type-py-method"><span class="n">LearningCurveDisplay</span><span class="o">.</span><span class="n">from_estimator</span></a><span class="p">(</span><span class="n">kr</span><span class="p">,</span> <span class="o">**</span><span class="n">common_params</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Learning curves"</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">handles</span><span class="o">=</span><span class="n">ax</span><span class="o">.</span><span class="n">get_legend_handles_labels</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="s2">"SVR"</span><span class="p">,</span> <span class="s2">"KRR"</span><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_kernel_ridge_regression_003.png" srcset="../../_images/sphx_glr_plot_kernel_ridge_regression_003.png" alt="Learning curves" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> ( 0 minutes 8.198 seconds)</p>
<div class="sphx-glr-footer sphx-glr-footer-example docutils container" id="sphx-glr-download-auto-examples-miscellaneous-plot-kernel-ridge-regression-py">
<div class="binder-badge docutils container">
<a class="reference external image-reference" href="https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.2.X?urlpath=lab/tree/notebooks/auto_examples/miscellaneous/plot_kernel_ridge_regression.ipynb"><img alt="Launch binder" src="../../_images/binder_badge_logo23.svg" width="150px" /></a>
</div>
<div class="sphx-glr-download sphx-glr-download-python docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/1dcd684ce26b8c407ec2c2d2101c5c73/plot_kernel_ridge_regression.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_kernel_ridge_regression.py</span></code></a></p>
</div>
<div class="sphx-glr-download sphx-glr-download-jupyter docutils container">
<p><a class="reference download internal" download="" href="../../_downloads/9d2f119ab4a1b6f1454c43b796f2c6a6/plot_kernel_ridge_regression.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_kernel_ridge_regression.ipynb</span></code></a></p>
</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 - 2023, scikit-learn developers (BSD License).
<a href="../../_sources/auto_examples/miscellaneous/plot_kernel_ridge_regression.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>
$(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');
var hide_text = 'Hide prompts and outputs';
var show_text = 'Show prompts and outputs';
// create and add the button to all the code blocks that contain >>>
div.each(function(index) {
var jthis = $(this);
if (jthis.find('.gp').length > 0) {
var button = $('<span class="copybutton">>>></span>');
button.attr('title', hide_text);
button.data('hidden', 'false');
jthis.prepend(button);
}
// 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>');
});
// define the behavior of the button when it's clicked
$('.copybutton').click(function(e){
e.preventDefault();
var button = $(this);
if (button.data('hidden') === 'false') {
// hide the code output
button.parent().find('.go, .gp, .gt').hide();
button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'hidden');
button.css('text-decoration', 'line-through');
button.attr('title', show_text);
button.data('hidden', 'true');
} else {
// show the code output
button.parent().find('.go, .gp, .gt').show();
button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'visible');
button.css('text-decoration', 'none');
button.attr('title', hide_text);
button.data('hidden', 'false');
}
});
/*** 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>