Related papers: MAP Complexity Results and Approximation Methods
Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is…
In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): the problem of finding a mapping of a request graph (describing a workload) onto a substrate graph (describing the physical…
This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…
Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…
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…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
The growing reliance on artificial intelligence in safety- and security-critical applications is raising concerns about the robustness of neural networks to erroneous or adversarial input. Certification is a methodology for ensuring model…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for inverse…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of…
In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with a highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under…
In this paper, an exact bitwise MAP (Maximum A Posteriori) estimation algorithm for group testing problems is presented. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-disjunctive…
We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…
This paper addresses the adaptive radar target detection problem in the presence of Gaussian interference with unknown statistical properties. To this end, the problem is first formulated as a binary hypothesis test, and then we derive a…