arXiv research

Identity testing for reversible Markov chains without symmetry assumption.

New sampling and identity-testing methods for mixtures of distributions that don't satisfy approximate tensorization of entropy.

Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.

A new method simulates a lazy version of a Markov chain for empirical inference.

In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product distributions over $\{\pm 1\}^{d}$. Our testers have improved sample complexity compared to …

We study distribution testing with communication and memory constraints in the following computational models: (1) The {\em one-pass streaming model} where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and (2) A {\em distributed model} where the data samples reside at mul…

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i$'s are …

Different optimizer choices lead to different financial model predictions.

We study the problem of identity testing of markov chains. In this setting, we are given access to a single trajectory from a markov chain with unknown transition matrix $Q$ and the goal is to determine whether $Q = P$ for some known matrix $P$ or $\text{Dist}(P, Q) \geq ε$ where $\text{Dist}$ is suitably defined. In r…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size $k$ and desired…

Optimized testing of discrete distributions using predicted data.

Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general qualitative assumptions, such as independence or finite memory, clearly fail. Howe…

Efficiently estimate Boolean product distribution parameters from truncated samples.

We show that the square Hellinger distance between two Bayesian networks on the same directed graph, $G$, is subadditive with respect to the neighborhoods of $G$. Namely, if $P$ and $Q$ are the probability distributions defined by two Bayesian networks on the same DAG, our inequality states that the square Hellinger di…

New property helps SGD learn sparse functions efficiently in neural networks.