Related papers: On Negative Dependence Properties of Latin Hypercu…
In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…
We prove the main conjecture from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the metric dependence…
A general structural equation model is fitted on a panel data set that consists of $I$ correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
How can you sample good negative examples for contrastive learning? We argue that, as with metric learning, contrastive learning of representations benefits from hard negative samples (i.e., points that are difficult to distinguish from an…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
Given a hypergraph $\Gamma=(\Omega,\mathcal{X})$ and a sequence $\mathbf{p} = (p_\omega)_{\omega\in \Omega}$ of values in $(0,1)$, let $\Omega_{\mathbf{p}}$ be the random subset of $\Omega$ obtained by keeping every vertex $\omega$…
The frequency-dependent conductivity is studied for both the one-dimensional Hubbard model and a model of spinless fermions, using a selection rule, the Bethe ansatz energy eigenstates, and conformal invariance. For densities where the…
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
Labeling training data is a key bottleneck in the modern machine learning pipeline. Recent weak supervision approaches combine labels from multiple noisy sources by estimating their accuracies without access to ground truth labels; however,…
The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
A Greek weight associated to a parameterized random variable $Z(\lambda)$ is a random variable $\pi$ such that $\nabla_{\lambda}E[\phi(Z(\lambda))]=E[\phi(Z(\lambda))\pi]$ for any function $\phi$. The importance of the set of Greek weights…
We consider a $d$-dimensional correlated percolation problem of sites {\em not} visited by a random walk on a hypercubic lattice $L^d$ for $d=3$, 4 and 5. The length of the random walk is ${\cal N}=uL^d$. Close to the critical value…
We explore how local, cosmology-independent measurements of the Hubble constant and the age of the Universe help to provide a powerful consistency check of the currently favored cosmological model (flat LambdaCDM) and model-independent…
Metric learning is an important problem in machine learning. It aims to group similar examples together. Existing state-of-the-art metric learning approaches require class labels to learn a metric. As obtaining class labels in all…
The ability of learning disentangled representations represents a major step for interpretable NLP systems as it allows latent linguistic features to be controlled. Most approaches to disentanglement rely on continuous variables, both for…