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.

3322 questions
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Perceptron exercise

I wonder how to find a solution to the following questions: Q: Design a two-input perceptron that implements the boolean function A ∧¬ B? Q: Design a two-layer network of perceptrons that implements A XOR B. Q: If it's possible to design one-layer…
user16168
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Vapnik-Chervonenkis theory: growth function

A classification problem is considered with observations $x \in \mathbb{R}^2$ and responses $y \in \{0,1\}$. There is a set of axis-aligned rectangle classifiers $F$. Particularly, сlassifier $f_{a,b} \in F$ is defined so: if $a_1 \le x_1 \le b_1…
Sergey
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Hopfield Network?

I have a question about the formation of weight matrix in Hopfield network: Why is not considered self-loop (i.e. $w_{ii}=0$)? Can anyone help me in the issue? Thanks in advance!
Royana
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Why are kernel methods with RBFs effective for handwritten digits (letters) classification?

The question emerged while reading Ch. 3 of Rasmussen & Williams http://www.gaussianprocess.org/gpml/. In the end of this chapter, the authors gave results for the problem of handwritten digits classification (16x16 greyscale pictures); features are…
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Different penalty for support vector machine

here comes a question about the penalty for different groups in SVM. The data is to be separated into two classes, one is class A and one is class B. In traditional SVM, a wrong classification in A is taken the same with a wrong classification in…
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Check My Solution -> Problem: Deriving Bias term in the context of Support Vector Machines given the Weight Vector.

Please check my solution/understanding of deriving the bias term in the context of Support Vector Machines. Information given, (1.) $t_i(\mathbf{w}^T\mathbf{x}_i + b)=1$ (2.) $\mathbf{w} = \sum_{i=1}^{N} a_i t_i \mathbf{x}_i$ (3.) Kernel Function:…
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Correct way to substitute variable in an equality

Help me understand this part in proving a theorem relating to Rademacher complexity. For simplicity, I am going to avoid all extraneous variables (Eq (4)). Random variable $\psi(S)$ is written as $\psi$ for simplicity. Here $S$ is a sample set, $t$…
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Stationary policy assumption in Bellman equation.

I was checking the proof for the following lemma: Lemma. Suppose that $\pi$ is a stationary policy. Then $V^π$ and $Q^π$ satisfy the following Bellman consistency equations: for all $s \in S$ and $a \in A$, \begin{align} V^{\pi}(s) &= Q^{\pi}(s,…
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Why is part of the hinge loss convex?

In section 12.3 of Understanding Machine Learning: From Theory to Algorithms, it is stated that the hinge loss, $l^{hinge} = max \{0, 1 - y \}$ is convex. It is stated that the hinge loss is convex because of claim 12.5. Claim 12.5 basically…
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Sufficient statistic mapping into a Hilbert space

I am currently working on my bachelor thesis and I came across a sufficient statistic, φ : X × Y → H of y | x where X is a candidate set in this case strings, Y is a binary property space: {-1,1}, H is a Hilbert Space. I understand that φ is…
RandomName101
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VC dimension of $ \{ 1_{b_1 g_1(x) + \cdots + b_d g_d(x) \geq 0} , b_1, b_2 , \dots, b_d \in \mathbb{R} \}$

I am new to VC dimension. I have to show that : Let $g_1, \cdots, g_d$ : $\mathcal{X} \rightarrow \mathbb{R}$ arbitrary : show that : $\mathcal{H} = \{ 1_{b_1 g_1(x) + \cdots + b_d g_d(x) \geq 0} , b_1, b_2 , \dots, b_d \in \mathbb{R} \}$ has VC…
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Loss Function Clarification

I'm learning about Machine Learning by writing proofs for derivatives of machine learning operations (like matrix multiplication, softmax, etc). I've started working on Loss Functions, but I've found the information online to be contradictory. I've…
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What is the growth function of the hypothesis set of linear classifiers on $\mathbb{R}^2$?

Recently I've been studying machine learning. I want to find out the growth function of the following hypothesis set: $$ \mathcal{H}=\left\{h_\mathbf{w}\equiv\mbox{sign}\big(\langle\mathbf{w}, \cdot\rangle\big)\,\colon…
yanruijie
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Kernel density estimators in Bishop book unclear formulas

In Bishop's book (Pattern recognition and machine learning, pag 122) there is an unclear passage for me in deriving certain formulas: $E[K/N] = P$ and $var[K/N] = P(1-P)$ Considering binomial probability $P(x=x) = \binom{N}{x} P^{x} \cdot (1 -…
Gianni
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Unclear formula in the book of linear model for classification in the Bishop book (machine learning)

From Bishop's book pag 183 - (4.11) (Pattern Recognition and Machine Learning, 2009), a mathematical relationship is immediately shown without an explanation of where it is derived from: I cannot understand where 4.11 comes from and the meaning of…
Gianni
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