# Questions tagged [machine-learning]

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### Uniform Lipschitz function approximation by shallow neural networks

Fix $d\in \mathbb{N}$. Let $F_1$ be the set of all 1-Lipschitz functions mapping $[0, 1]^d$ to $\mathbb{R}$. For $\varphi: \mathbb{R} \rightarrow \mathbb{R}$ and $m \in \mathbb{N}$, let $N_\varphi^m$ ...
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### Independence in a sequential problem with observations getting added to buckets

Consider a sequence of random observations $(O(t))_{t\geq 1}$, with $O(t)=(D(t),J(t),Y(t))$. Denote $\mathcal{F}(t) := \sigma(O(1),\ldots,O(t))$, the filtration induced by the first $t$ observations. ...
120 views

### Books to develop a unified view of statistics and information theory?

I hope to understand the connection between statistics and information theory in a deep philosophical sense. I suppose the best place to start would be David MacKay's Information Theory, Inference, ...
161 views

### Abstract mathematical concepts/tools appeared in machine learning research

I am interested in knowing about abstract mathematical concepts, tools or methods that have come up in theoretical machine learning. By "abstract" I mean something that is not immediately related to ...
93 views

### Inequality on the Kullback-Leibler divergence

Let us define the arithmetic, geometric, and harmonic means of $x,y \in \mathbb{R}$ weighted by $\alpha =(\alpha_x,\alpha_y) \in [0,1]$, respectively as \begin{equation} a_\alpha(x,y) = \frac{\...
138 views

### Statistical divergence

Does anyone know about a statistical divergence of this type? \begin{equation} \text{D}(P||Q) = \frac{1}{2} \left[\text{KL}(M||P) + \text{KL}(M||Q)\right] \end{equation} where $M = \frac{1}{2} [P+Q]$....
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### Comparison of concentrations of different $L^p$-norms of (sub) Gaussian distributions

It's well-known that the Euclidean $2$-norm of subgaussian random vectors concentrates in high dimensions, e.g. when $X \sim \mathcal{N}(0,I_n),$ (or in general $X$ is subgaussian with independent co-...
160 views

### Help with a definition of a two-person game in a referenced paper

In the paper "Finding Mixed Nash Equilibria of Generative Adversarial Networks" the authors write in equation (1) on page 2: Consider the classical formulation of a two-player game with finitely ...
29 views

### What is the number of iterations needed for the message passing algorithm to converge when applied to an acyclic factor graph?

I understand that the message passing algorithm (Belief Propagation algorithm), when applied to a factor graph consists in an exchange in messages between the factor nodes and the variable nodes, ...
2k views

### mathematical physics without partial derivatives

Remark: All the answers so far have been very insightful and on point but after receiving public and private feedback from other mathematicians on the MathOverflow I decided to clarify a few notions ...
46 views

### Variational forms of non-convex functions

I am trying to understand what kind of variational forms exist for non-convex functions. Alternatively, are there conjugate forms which attain strong duality? For a non-convex function $f$, I am ...
28 views

### sequential learning reference request [closed]

I would like to find a book for master math student about the following topics. I don't know the field and I don't want to be lost in details so if it could be an straight forward please. I'm a ...
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### What subjects of Fourier analysis have had more effect on machine learning? [closed]

What is the salient uses of Fourier analysis in machine learning? What subjects of Fourier analysis have had more effect on machine learning? Please mention the references.
163 views

### Statistical model vs. Statistical Learning Theory

I am interested in the relation between a statistical model $(\Omega, \mathcal{F}, (\mathbb{P}^\theta : \theta\in\Theta))$, where the hypotheses are "$\mathbb{P}^\theta$ is a good approximation of the ...
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### Plethora of variant neural networks?

Since a decade ago when new life was breathed in to neural networks in the form of deep learning a plethora of different architectures have come about. Is there a reference that gives compendium of ...
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