Related papers: Complexity Results and Approximation Strategies fo…
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…
In recent years, researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature,…
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected…
In this paper we study the {\it bilinear assignment problem} (BAP) with size parameters $m$ and $n$, $m\leq n$. BAP is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
The theoretical models providing mathematical abstractions for several significant optimization problems in machine learning, combinatorial optimization, computer vision and statistical physics have intrinsic similarities. We propose a…
Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the variables. A solution to such a…
Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…