# 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?

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### Optimizing function defined by integral

Let the two functions $q: \mathbb{R}^d \rightarrow\mathbb{R}^{+}$ and $s: \mathbb{R^d} \times \mathbb{R^d} \rightarrow \mathbb{R}^{+}$, $d \in \mathbb{N,}$ where both are assumed to be continuous and ...
525 views

### Large Deviation, Optimal Transport and Machine Learning Reference

I am looking for references (books/sites/articles) on the following three subjects: Large Deviation, Optimal Transport and Machine Learning References. I would like works which involve any of them ...
1 vote
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### $\min$-entropy for the uniform distribution on $[𝑛]$

The min-entropy of a distribution $\nu$ on $[n]$ is given as: $$H_{\infty}(\nu)=\min_{i} \log(\frac{1}{\nu(i)})$$ Now we will prove that that for every distribution $\nu$ on $[n]$ and for $U$ being ...
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### variance maximization in PCA: doubt for the correctness of an Algerian passage.

I know trying to perform the steps omitted in Bishop's machine learning book (from point 12.4 to 12.5): there is only one step that leaves me with a doubt of correctness namely whether I can, taken ...
162 views

### ODE's: Continuity Equation

The context of this question is Machine Learning (more specifically, my question results from this paper, yet I have a math question, so I'm posting it here). First of all, some definitions (Sec. 2 of ...
1 vote
108 views

### Shapley Kernel Proof

I read the paper about SHAP. I think this paper is very interesting ! I would like to understand the algorithm, but I cannot follow the below fact. \begin{equation} X^T WX=\dfrac{1}{M-1}I+cJ \end{...
1 vote
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### Unclear maximization step in the PCA for machine learning [closed]

In Bishop's book (Pattern Recognition and Machine Learning, chapter PCA) there is this passage for calculating the gradient with respect to $\vec{u}_{1}$. In the passage, $\vec{u}_{1}^{T}$ are ...
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### How to make the income distribution of a country follows the 80:20 rule?

My main question: Let's imagine a country with a population of $n$ people. Each person has a certain amount of income in a certain year. When we calculate the income distribution of this country, we ...
19 views

### How is this reinforcement learning value formula read / understood?

$$V_\pi(s) = E[R_t|s_t=s,\pi]$$ This is a value function for state s under policy $\pi$ where $R_t$ is the return value, all of which occurs at time t. I was wondering how I should read/ understand ...
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### VC dimension of indicator functions is equal to pseudo dimension

I am reading the "Foundation of machine learning" by Mehryar Mohri (https://cs.nyu.edu/~mohri/mlbook/). In the proof of Theorem 11.8, it said the following statement, which I can not ...
27 views

### Limiting probability of classifying correctly with the k-NN algorithm as the number of data points increases.

Let $x_1, \ldots, x_n$ be random variables that are uniformly distributed on [0,2]. If $x_i \leq 1$, we'll classify it as green ($y_i=0$), and if $x_i > 1$, we'll classify it as red ($y_i=1$). We ...
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### KKT Conditions for SVM Problem

I am reading about SVMs and want to confirm that I understand the optimality conditions. Details below: Consider the $n$ points $x_1, x_2, \dots, x_n$, each with $d$ dimensions, and consider $n$ ...
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### Finding an algorithm EF[1,1] and PO division for more than two agents

From this research paper I want to write an algorithm for finding envy-freeness(EF) and Pareto optimality(PO) division for more than two agents. We consider the problem of fairly and efficiently ...
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### Maximizing the summation of reward of some users (waiting in different positions and lines) using reinforcement learning or other learning methods

There is a mathematical problem that I think can be solved using reinforcement learning and it would be great if you could help me with it. Some users are standing in some lines. There are N lines. In ...
37 views

### Recommendations for Information Geometry in Machine Learning

I am fairly new to machine learning, but I have a 22-dimensional dataset, which I would like to increase the interpretability of by dimension reduction. I am relatively familiar with principal ...
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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 ...
1 vote
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1 vote
37 views

### Coefficient for the gradient term in stochastic gradient descent (SGD) with momentum

I'm studying SGD with momentum and have come across two versions of the update formula. The first is from a wiki same as from the original paper:  \Delta w^t = \alpha * \Delta w^{t-1} - lr * \nabla ...
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### Does skipgram model uses backpropagation? [migrated]

I just started to get interested in natural language processing and I was trying to understand the skipgram model from word2vec. I was reading this interesting website. However, in the mentioned ...
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### Is this a closed-form analytical solution for the hard-margin SVM dual problem?

I have been searching, without much success, for some dicussion on the possibilities (or impossibilities) of a general closed-form analytical solution for the hard-margin (only) support vector ...
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### Similarity metric between two sets of points with varying densities

How can I create a similarity metric that describes the top left set of points as more similar to the bottom left set of points than the top right set of points? Clearly least-squares distance doesn't ...
50 views

### How can I understand the (no) independence property in this very simple setting of first order logic?

My understanding of logic is limited to first order logic without functions with finite set of domain constants, and with herbrand semantics. Now in this setting, I would like to understand the ...
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### Implementing multiclass logistic regression from scratch

This is a sequel to a previous question about implementing binary logistic regression from scratch. Background knowledge: To train a logistic regression model for a classification problem with $K$ ...