Related papers: A Simple Algorithm for Exact Multinomial Tests
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
We show that computing even very coarse approximations of critical points is intractable for simple classes of nonconvex functions. More concretely, we prove that if there exists a polynomial-time algorithm that takes as input a polynomial…
We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\dots,x_n)$ over $R^n$ and a parameter $\epsilon> 0$, our…
We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…
Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
In genetic association studies, detecting disease-genotype associations is a primary goal. For most diseases, the underlying genetic model is unknown, and we study seven robust test statistics for monotone association. For a given test…
In Siotani & Fujikoshi (1984), a precise local limit theorem for the multinomial distribution is derived by inverting the Fourier transform, where the error terms are explicit up to order $N^{-1}$. In this paper, we give an alternative…
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…
We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…