Questions tagged [machine-learning]

How can we build computer systems that automatically improve with experience, and what are the fundamental laws that govern all learning processes?

From The Discipline of Machine Learning by Tom Mitchell:

The field of Machine Learning seeks to answer the question "How can we build computer systems that automatically improve with experience, and what are the fundamental laws that govern all learning processes?" This question covers a broad range of learning tasks, such as how to design autonomous mobile robots that learn to navigate from their own experience, how to data mine historical medical records to learn which future patients will respond best to which treatments, and how to build search engines that automatically customize to their user's interests. To be more precise, we say that a machine learns with respect to a particular task T, performance metric P, and type of experience E, if the system reliably improves its performance P at task T, following experience E. Depending on how we specify T, P, and E, the learning task might also be called by names such as data mining, autonomous discovery, database updating, programming by example, etc.

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What is the VC dimension of a d-dimensional quadratic function?

I have an indicator function $I(M, x, y) = sign[(M(x - u))^{T} (M(x - u)) - y]$. $M$ is an invertible matrix of size $d \times d$. $x, u$ are vectors of size $d$. $u$ is a parameter for the indicator function. $y \in \mathcal{R}$. What is the VC…
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VC Dimension for Non Linear Models

For non linear models like neural networks the number of VC dimensions could be larger then the number of parameters. Is this a correct statement , I tried looking for leads but was not able to find any good ones. Any pointers or explanation would…
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Help with Training and Testing Classifier errors

I am trying to understand if classifier X has smaller training error than classifier Y, then classifier X will have smaller generalization (test) error than classifier Y. ( Answer is False) My understanding is below: They can be totally…
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Proving concavity of a function in multiple variables

How do I prove that $f(\vec{x}) = \vec{b}.\vec{x} - \log \left (1+e^{\vec{a}.\vec{x}} \right )$ is concave? where $\vec{a}$ and $\vec{b}$ are constant vectors. My steps are as follows: The first term is a linear function in $\vec{x}$ so the first…
rims
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Possible Growth Function for a hypothesis set

I am new to machine learning and I am trying to resolve a homework problem. How do I determine the possible growth function $mH(N)$ for some hypothesis set? My choices are $1,2^N,2^\sqrt{N},N^2-N+2$ and none. My research : I understand that the…
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Normalize numerical values

In a AI course, we have to normalize a set of numerical inputs such that the highest input becomes $1$ and the lowest becomes $0$. The set is as follows: $ 1\\3\\5\\2 $ So the first entry should become $0$ and the third one becomes $1$. Now how do I…
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Meaning "unique nearest neighbour" (k-NN)

I'm doing an exercise about k-NN, k-Neighbor classifier. And I don't understand the following sentence: Show that for all x ∈ $R^d$ which have a unique nearest neighbor amongst the points in {x1, . . . , xn} there exists an $h_0 > 0$ such that…
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Estimate the Vapnik Chervonenkis dimension

Accourding to theorem 5 of Dr Edgard's paper can be estimated with the function $O(ρ^2)$ Theorem 5. The class of functions computed by multilayer neural networks with binary as well as linear activations and ρ weights has VC dimension $O(ρ^2)$. My…
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Principal Component Analysis on a Dataset

I have a dataset with 20 feature columns, 1 label column, and 1200 samples. I have to test an MLP classifier on this dataset. Does it make sense to apply PCA before using the MLP, given the fact that all the feature columns have a similar…
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How to find a support vector machine by hand with only a few data points?

Given data points x1, x2 and their classifications y in the form (x1, x2, y), 1) How do I know which points are support vectors? 2) How do I find the support vector classifier by hand including the weight and bias? 3) How do I find the margin? The…
Bobby
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Understanding extended perceptron

I am new to machine learning and could understand the simple perceptron. I came to a formula while reading about perceptron. $$ y = \sum_{k = 1}^{K}z_{k}(x)(\Theta _{0}^{(k)} + \sum_{j = 1}^{m}\Theta _{j}^{(k)}x_{j}) $$ where $$ z_{k}(x) \epsilon…
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Why are features weighted in machine learning?

I would like to ask why features are weighted in machine learning before activation? Could you explain this on very simple and practical example?
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stochastic gradient descent

Hello i am reading the book the elements of statistical learning by hastie tibshirani and friedman https://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf. I am stuck at the page 131 and the equation 4.42. I dont unterstand, to…
Felix Ha
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Non-overlapping densities

I have come across the following argument concerning the Bayes error: Let $r(x)=\mathbb{E}[Y|X=x]$ be the regression of $Y$ on $X$. Then one can show that the Bayes error is $L^* = \mathbb{E}[\min(r(X),1-r(X))]$. Suppose now that $X$ has a…
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Normalisation techniques for largely variate feature values..

I have a set of feature values in a matrix where a single column represents feature values for each 3D point (i.e. each row). I need to use that data for training a SVM model. For doing that, I first need to normalize the feature values. But the…