Related papers: Maximum A Posteriori Inference in Sum-Product Netw…
We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine…
Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22],…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is…
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often…
MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…
Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…
A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and…
We study the computational complexity of two hard problems on determinantal point processes (DPPs). One is maximum a posteriori (MAP) inference, i.e., to find a principal submatrix having the maximum determinant. The other is probabilistic…
Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel…
The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor…