Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
An introduction of statistical learning
Search
Nakamura, Ryotaro
June 28, 2017
Science
0
34
An introduction of statistical learning
Nakamura, Ryotaro
June 28, 2017
Tweet
Share
More Decks by Nakamura, Ryotaro
See All by Nakamura, Ryotaro
Duct for beginners.
nryotaro
0
4k
Learn Go in 15 minutes
nryotaro
0
33
Seven architectural patterns
nryotaro
1
94
Improving Performance with Parallel Programming
nryotaro
0
44
Other Decks in Science
See All in Science
Pericarditis Comic
camkdraws
0
1.5k
02_西村訓弘_プログラムディレクター_人口減少を機にひらく未来社会.pdf
sip3ristex
0
160
Planted Clique Conjectures are Equivalent
nobushimi
0
120
ウェーブレットおきもち講座
aikiriao
1
830
多次元展開法を用いた 多値バイクラスタリング モデルの提案
kosugitti
0
240
The thin line between reconstruction, classification, and hallucination in brain decoding
ykamit
1
1.2k
Celebrate UTIG: Staff and Student Awards 2024
utig
0
590
All-in-One Bioinformatics Platform Realized with Snowflake ~ From In Silico Drug Discovery, Disease Variant Analysis, to Single-Cell RNA-seq
ktatsuya
0
310
オンプレミス環境にKubernetesを構築する
koukimiura
0
130
Online Feedback Optimization
floriandoerfler
0
930
Introduction to Image Processing: 2.Frequ
hachama
0
480
Coqで選択公理を形式化してみた
soukouki
0
290
Featured
See All Featured
JavaScript: Past, Present, and Future - NDC Porto 2020
reverentgeek
47
5.2k
Bash Introduction
62gerente
611
210k
Exploring the Power of Turbo Streams & Action Cable | RailsConf2023
kevinliebholz
30
4.6k
How to Create Impact in a Changing Tech Landscape [PerfNow 2023]
tammyeverts
49
2.3k
Understanding Cognitive Biases in Performance Measurement
bluesmoon
27
1.6k
Writing Fast Ruby
sferik
628
61k
It's Worth the Effort
3n
184
28k
Testing 201, or: Great Expectations
jmmastey
42
7.2k
4 Signs Your Business is Dying
shpigford
183
22k
Measuring & Analyzing Core Web Vitals
bluesmoon
6
260
Code Review Best Practice
trishagee
67
18k
StorybookのUI Testing Handbookを読んだ
zakiyama
28
5.5k
Transcript
ػցֶशษڧձ ୈ 1 ճ தଜ ྒྷଠ June 13, 2017
Table of contents Supervised Learning 1. Classification 2. Perceptron 3.
Regression Unsupervised Learning 4. Clustering 1
ࠓͷඪ ࣍ճҎ߱ʹֶͿΞϧΰϦζϜͷ֓ཁΛΔ ΞϧΰϦζϜͱద༻ྫ ΞϧΰϦζϜ ద༻ྫ ྨ εύϜϝʔϧఆ ճؼੳ ച্༧ଌ ΫϥελϦϯά
ը૾ͷݮ৭ॲཧ 2
ύϥϝτϦοΫ๏ ϞσϧʢࣜʣΛԾఆ͠ɼϞσϧͷ࠷దͳύϥϝλΛֶश͢Δ ύϥϝτϦοΫ๏ͷखॱ 1. σʔλͷ༧ଌϞσϧΛԾఆ 2. Ϟσϧͷύϥϝλͷ ධՁج४ΛܾΊΔ 3. ύϥϝλΛܾΊΔ
0.0 0.2 0.4 0.6 0.8 1.0 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Ұ࣍ؔͷϞσϧͷύϥϝλௐ 3
Classification
ྨ Ϋϥεʹྨ͞ΕͨطଘσʔλΛݩʹ৽نσʔλΛྨ͢Δ ΞϧΰϦζϜ • ύʔηϓτϩϯ • ϩδεςΟοΫճؼ 4
Perceptron
ύʔηϓτϩϯ, Ϟσϧ ઢܗͳϞσϧ f Λઃఆ͢Δ f (x, y) = w0
+ w1x + w2y f (x, y) > 0 ⇒ t = +1 f (x, y) < 0 ⇒ t = −1 −20 −10 0 10 20 30 x −30 −20 −10 0 10 20 y t = +1 t = -1 ଐੑ t = ±1 Λͭσʔλ܈ ઢ্ͷ (x′, y′) f (x′, y′) = 0 ΛΈͨ͢ 5
ύʔηϓτϩϯ, ධՁج४ʢޡࠩؔʣ ޡࠩؔ E ͕࠷খʹͳΔ wi ΛٻΊΔ E = N
∑ i=1 {− (w0 + w1x + w2y) ti } = N ∑ i=1 (−f (xi , yi )ti ) • N σʔλ • ޡྨͩͱ −f (xi , yi )ti > 0 −20 −10 0 10 20 30 x −30 −20 −10 0 10 20 y t = +1 t = -1 ଐੑ t = ±1 Λͭσʔλ܈ 6
ϩδεςΟοΫճؼ, Ϟσϧ ύʔηϓτϩϯͱಉ͘͡ઢܗϞσϧ f Λઃఆ͢Δ f (x, y) = w0
+ w1x + w2y f (x, y) > 0 ⇒ t = +1 f (x, y) < 0 ⇒ t = −1 −30 −20 −10 0 10 20 30 x −20 −15 −10 −5 0 5 10 15 20 y t = +1 t = -1 f (x, y) ͕૿Ճ͢Δ͖ 7
ϩδεςΟοΫճؼ, Ϟσϧ ͨͩ͠ɼ|f | ͕େ͖͍΄Ͳ t Ͱ͋Δ͕֬ߴ͍ͱ͢Δ ϩδεςΟοΫؔ σ (α)
= 1 1 + e−α Λಋೖ͠ɼ (x′, y′) ͕ t = 1 Ͱ͋Δ֬Λ 0 < σ ( f ( x′, y′ )) < 1 ͱ͢Δ −4 −3 −2 −1 0 1 2 3 4 α 0.0 0.2 0.4 0.6 0.8 1.0 σ (α) ϩδεςΟοΫؔͷάϥϑ 8
ϩδεςΟοΫճؼ, ධՁج४ʢ࠷ਪఆʣ ܇࿅σʔλ͕ಘΒΕΔ֬ P Λ࠷େʹ͢Δ wi ΛٻΊΔ p(x, y) =
σ(x0 + w1x + w2y) P = N ∏ i p (xi , yi )tn {1 − p (xi , yi )}1−tn ܇࿅σʔλ࠷ൃੜ͕֬ߴ͍σʔλͰ͋ΔͱԾఆ͍ͯ͠Δ 9
Regression
ճؼੳ, ϞσϧͱධՁج४ʢ࠷খೋʣ σʔλ͕ M ࣍ଟ߲ࣜ f ʹै͏ͱͯ͠ɼೋޡࠩ ED Λ࠷খʹ͢Δ ύϥϝλ
wi ΛબͿ f (x) = M ∑ m=0 wmxm ED = 1 2 N ∑ n=1 {f (xn) − tn}2 0 2 4 6 8 10 −15 −10 −5 0 5 ground truth degree 3 degree 4 degree 5 training points M ∈ {3, 4, 5} ͷଟ߲ࣜۙࣅྫ 10
Clustering
k ฏۉ๏ σʔλؒͷڑΛٻΊɼσʔλΛ k ݸͷΫϥελʹ͚Δ −2 −1 0 1 2
3 0 1 2 3 4 5 σʔλू߹ −2 −1 0 1 2 3 0 1 2 3 4 5 cluster 1 cluster 2 cluster 3 centroids k = 3 ͷΫϥελ Ϋϥελ͝ͱʹදσʔλΛܾΊɼදͷۙ͘ͷσʔλू߹Ͱ ΫϥελΛ࡞Δ 11
k ฏۉ๏ͷΞϧΰϦζϜ ೖྗ: σʔλू߹ D = { x(1), x(2), ·
· · , x(|D|) } : Ϋϥελ k ແ࡞ҝʹ m1, m2 · · · , mk ΛܾΊΔ until ऩଋ foreach x(i) ∈ D cmax = arg max c sim ( x(i), mc ) σʔλू߹ͷׂ insert x(i)into cmax end foreach ∀c, mc = 1 |c| ∑ x(i)∈c x(i) දϕΫτϧΛ࠶ܭࢉ end until 12