Related papers: Algorithms and Hardness for Estimating Statistical…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
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 give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\Delta$ on $n$ vertices, for all $k \le (1-\delta)m^*(G)$, where $\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Motivated by multi-domain service function chain (SFC) orchestration, we define the shortest-longest path (SLP) problem, prove its hardness, and design an efficient fully polynomial time approximation scheme (FPTAS) using the dynamic…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
We introduce a conceptually simple and effective method to quantify the similarity between relations in knowledge bases. Specifically, our approach is based on the divergence between the conditional probability distributions over entity…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…