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We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We consider a system of $N$ particles whose interactions are characterized by a (weighted) graph $G^N$. Each particle is a node of the graph with an internal state. The state changes according to Markovian dynamics that depend on the states…
Suppose that we are given an arbitrary graph $G=(V, E)$ and know that each edge in $E$ is going to be realized independently with some probability $p$. The goal in the stochastic matching problem is to pick a sparse subgraph $Q$ of $G$ such…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
In this paper, we generalize the recently studied Stochastic Matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the Stochastic Matching problem that has…
The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…