# Questions tagged [machine-learning]

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### What's the probability of one binary classifier being better than another knowing the results on a sample of size N? [closed]

Assuming that classifier_1, classifier_2 have an unknown success rate α, β, what is the probability that α>β if after doing an experiment on a m.a.s of size 20 classifier_1 obtains a success rate ...
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### Matrix valued word embeddings for natural language processing

In natural language processing, an area of machine learning, one would like to represent words as objects that can easily be understood and manipulated using machine learning. A word embedding is a ...
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### Training an energy-based model (EBM) using MCMC

I'm reading this paper about training energy-based models (EBMs) and don't understand the parameters that we are training for? The part that is relevant to the question is in pages 1-4. Here is the ...
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### How are eigenvalues of two psd kernels related?

Suppose $K(x,x')$ and $R(y,y')$ are two positive semi-definite kernels on $(x,x')\in \mathbb {X}\times\mathbb{X}$ and $(y,y')\in\mathbb{Y}\times\mathbb{Y}$, respectively, and satisfying the following ...
1 vote
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### How to maximize certain function of hundreds variables related to correlations between sets vectors ? (and win Kaggle :))

It might be helpful for data science/bioinformatics challenge. Consider for simplicity three rectangular matrices $Y_{true}$ , $Y_{predict0},Y_{predict1}$ of the same sizes say 70000*140. Let us ...
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3 votes
1 answer
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### Independent input feature z can be removed: if y=f(x+z,z), then y=g(x)?

Let $y\in \mathbb{R}$ and $\mathbf{x},\mathbf{z}\in\mathbb{R}^p$ be random variable and random vectors. Assume $y=f(\mathbf{x}+\mathbf{z},\mathbf{z})$ for some function $f$. Is the following statement ...
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1 vote
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### Sample Complexity/PAC-Learning Notation

In PAC Learning, Sample Complexity is defined as: The function $m_\mathcal{H} : (0,1)^2 \rightarrow \mathbb{N}$ determines the sample complexity of learning $\mathcal{H}$: that is, how many examples ...
1 vote
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20 votes
3 answers
3k views

### How can Machine Learning help “see” in higher dimensions?

The news that DeepMind had helped mathematicians in research (one in representation theory, and one in knot theory) certainly got many thinking, what other projects could AI help us with? See MO ...
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### Covering/Bracketing number of monotone functions on $\mathbb{R}$ with uniformly bounded derivatives

I am interested in the $\| \cdot \|_{\infty}$-norm bracketing number or covering number of some collection of distribution functions on $\mathbb{R}$. Let $\mathcal{F}$ consist of all distribution ...
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### Limit cycles or stable solutions for k-dimensional piece-wise linear ODEs

As a branch of reinforcement learning, restless multi-armed bandits have been shown PSPACE-HARD but Whittle has offered an implementable solution called the Whittle Index Policy. Weber and Weiss ...
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### Correlating two matrices $A,B$ with stochastic dependency structure imposed by cross-validation

Consider a labelled data set $$D = \{(x_1, y_1),...,(x_n, y_n)\}$$ on which we want to evaluate a machine learning algorithm using $k$-fold cross validation with $m$ different random seeds. This ...
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2 votes
1 answer
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### How to fit a set of parametrized data to a parametrized distribution?

I have a time series $d_i(a)$ which depends on the parameter $a$. On the other hand, I have a sequence of normal distributions $\mathcal{N}(0,Q_i(a))$, where the variance $Q_i$ depends on time and ...
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### Stochastic gradient descent in 'stronger' settings

I am minimzing a function $F(x) = \mathbb E(f(x,\Xi))$ where $\Xi$ is some random value, by a stochastic gradient descent that generates a random number $\xi$ from the distribution of $\Xi$ at each ...
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### Mathematical questions or areas amenable to AI [duplicate]

This question regards the new paper "Advancing mathematics by guiding human intuition with AI" by Davies et al. (Nature, 2021) (DOI link in open access) in which researchers at Deepmind ...