Related papers: Low complexity, low probability patterns and conse…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Autonomous systems, like vehicles or robots, require reliable, accurate, fast, resource-efficient, scalable, and low-latency trajectory predictions to get initial knowledge about future locations and movements of surrounding objects for…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
In this work we study optimization problems subject to a failure constraint. This constraint is expressed in terms of a condition that causes failure, representing a physical or technical breakdown. We formulate the problem in terms of a…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational…
Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
With the emerging of new networks, such as wireless sensor networks, vehicle networks, P2P networks, cloud computing, mobile Internet, or social networks, the network dynamics and complexity expands from system design, hardware, software,…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…