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Results tagged with machine-learning
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user 10812
Machine learning algorithms build a model of the training data. The term "machine learning" is vaguely defined; it includes what is also called statistical learning, reinforcement learning, unsupervised learning, etc. ALWAYS ADD A MORE SPECIFIC TAG.
1
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1
answer
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Temporal difference definition (Reinforcement Learning)
Reading for instance Szepesvari or this : i struggle to understand the rationale behind the temporal-difference definition
$\delta_{t}=R_{t}+\gamma V_{k}(x_{t+1})-V_{k}(x_{t})$
with the notation fr …
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0
votes
0
answers
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Bernouilli variables - bias and variance of estimator
Reading through this I work on Example 1 in 3. Consistency.
$X_{1},... , X_{n} ∼ Bernoulli(p)$. The mle $\hat{p}$ has bias 0 and variance $p(1−p)/n \rightarrow 0$.
Here $\hat{p} =
\sum_{i} Xi/n$. So …
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2
votes
0
answers
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Bias Variance Decomposition 2.7 in Elements of Statistical Inference
I try to derive 2.7 from the book. I expose my demonstration
$E_\tau[(y_0-\hat{y}_0)^2]=E_\tau[y_0^2]-2E_{\tau}[y_{0}\hat{y_{0}}]+E_{\tau}[\hat{y_{0}}^{2}]$
$= y_{0}^{2}-2y_{0}E_{\tau}[\hat{y_{0}}]+E …
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2
votes
1
answer
4k
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Array of samples from multivariate gaussian distribution Python [closed]
I am trying to build in Python the scatter plot in part 2 of Elements of Statistical Learning. First it is said to generate
10 means mk
from a bivariate Gaussian distribution N((1,0)T,I) and lab …
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0
votes
Accepted
Prove that the direction in Least Angle Regression makes equal angle with all predictors
The fit direction at step $k$ is $u_{k}=X_{A_{k}}\delta_{k}$ where $\delta_{k}=(X^{T}_{A_{k}}X_{A_{k}})^{-1}X^{T}_{A_{k}}r_{k}$. Thus we have $X_{A_{k}}^{T}u_{k}=X_{A_{k}}^{T}X_{A_{k}}\delta_{k}=X_{A_ …
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3
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1
answer
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Finding optimal subspace for Linear Discriminant Analysis - Elements of Statistical Learning...
Linear Discriminant Analysis (LDA) possibly operates a dimension reduction. Section 4.3.3 in Elements of Statistical Learning explicits this notion as well as a method for computing the "optimal subsp …
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2
votes
Accepted
Finding optimal subspace for Linear Discriminant Analysis - Elements of Statistical Learning...
Within-class, between-class covariance matrices
• Assuming common covariance matrix $\hat{\Sigma}=\hat{\Sigma}_{k}$ for all classes $k$ we write
$\hat{\Sigma}=\sum_{k=1}^{K}\sum_{g_{i}=k}{(x_{i}-\ha …
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0
votes
1
answer
251
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Prove that the direction in Least Angle Regression makes equal angle with all predictors [closed]
Least Angle Regression iteralively adds predictors according to the procedure described here : Writing by hand first steps in Least Angle Regression (LARS)
We note $A_{k}$ the active set of variables …
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4
votes
1
answer
832
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Linear Discriminant Analysis - deriving classifier expression for multivariate normal distri...
From Elements of Statistical Learning chap 4 - https://web.stanford.edu/~hastie/Papers/ESLII.pdf
We have K classes and we are modeling the posterior probability : $P(G=k|X=x)=\frac{f_{k}(x)\pi_{k}}{\ …
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3
votes
1
answer
92
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Rationale behind Q-learning
I am reading Sutton Barto on Reinforcement Learning. I understand that $TD(\lambda)$ methods propose better performance than Monte Carlo methods, with TD methods combining advantages of Dynamic Progra …
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3
votes
1
answer
571
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Computation of LDA in Elements of Statistical Learning 4.3.2
Elements of Statistical Learning 4.3.2 elaborates on computation for Linear Discriminant Analysis. https://web.stanford.edu/~hastie/Papers/ESLII.pdf
Procedure is said to be
• Sphere the data wit …
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Accepted
Computation of LDA in Elements of Statistical Learning 4.3.2
Sphering ( or whitening ) the data ($X$) means applying a transformation so that in the new basis, the covariance for sphered data ($X^{*}$) is the identity matrix, i.e. $E[X^{*T}X^{*}]=I_{n}$ .
We op …
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