Related papers: Computing Upper and Lower Bounds on Likelihoods in…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
Provided an arbitrary nonintrusive load monitoring (NILM) algorithm, we seek bounds on the probability of distinguishing between scenarios, given an aggregate power consumption signal. We introduce a framework for studying a general NILM…
Predicting missing links in real networks is an important problem in network science to which considerable efforts have been devoted, giving as a result a vast plethora of link prediction methods in the literature. In this work, we take a…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
In this paper, we analyze the monotone space of complexity of directed connectivity for a large class of input graphs $G$ using the switching network model. The upper and lower bounds we obtain are a significant generalization of previous…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…
Inference algorithms for arbitrary belief networks are impractical for large, complex belief networks. Inference algorithms for specialized classes of belief networks have been shown to be more efficient. In this paper, we present a…
Qualitative possibilistic networks, also known as min-based possibilistic networks, are important tools for handling uncertain information in the possibility theory frame- work. Despite their importance, only the junction tree adaptation…
Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…
We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
Computing the cut-set bound in half-duplex relay networks is a challenging optimization problem, since it requires finding the cut-set optimal half-duplex schedule. This subproblem in general involves an exponential number of variables,…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…
In practice, since many communication networks are huge in scale or complicated in structure even dynamic, the predesigned network codes based on the network topology is impossible even if the topological structure is known. Therefore,…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…
Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…