Related papers: Counting solutions from finite samplings
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the…
Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data…
Modeling symptom progression to identify informative subjects for a new Huntington's disease clinical trial is problematic since time to diagnosis, a key covariate, can be heavily censored. Imputation is an appealing strategy where censored…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
Question-answering systems and voice assistants are becoming major part of client service departments of many organizations, helping them to reduce the labor costs of staff. In many such systems, there is always natural language…
We show for a broad class of counting problems, correlation decay (strong spatial mixing) implies FPTAS on planar graphs. The framework for the counting problems considered by us is the Holant problems with arbitrary constant-size domain…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Purpose: The scattering phenomenon creates degrading effects in positron emission tomography (PET) and the corresponding events are rejected conventionally. We have proposed a mathematical model to retrace the original line of response of…
We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number…
Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
We consider the problem of detecting the locations of targets in the far field by sending probing signals from an antenna array and recording the reflected echoes. Drawing on key concepts from the area of compressive sensing, we use an…