Related papers: Optimal Upper and Lower Bounds for Boolean Express…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
A major impediment towards the industrial adoption of decentralized distributed systems comes from the difficulty to theoretically prove that these systems exhibit the required behavior. In this paper, we use probability theory to analyze a…
Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two…
We develop a new probabilistic method for deriving deviation estimates in directed planar polymer and percolation models. The key estimates are for exit points of geodesics as they cross transversal down-right boundaries. These bounds are…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or…
We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served values, we propose a different estimate, the high-profile…
In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly,…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…
Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a…
A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…
We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…