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A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
Many problems reduce to the fixed-point problem of solving $x=T(x)$. To this problem, we apply the coordinate-update algorithms, which update only one or a few components of $x$ at each step. When each update is cheap, these algorithms are…
We recently reported that the simple genetic algorithm (SGA) is capable of performing a remarkable form of sublinear computation which has a straightforward connection with the general problem of interacting attributes in data-mining. In…
One of the most interesting questions about a group is if its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists and geometers, and is the target of intensive…
Knot-based, sparse Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Problems can occur, however, when knot selection is done by optimizing the marginal likelihood. For example, the…
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…
We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…
We present an algorithmic approach to the conjugacy problems in monoids, using rewriting systems. We extend the classical theory of rewriting developed by Knuth and Bendix to a rewriting that takes into account the cyclic conjugates.
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…
We introduce a batched lazy algorithm for supervised classification using decision trees. It avoids unnecessary visits to irrelevant nodes when it is used to make predictions with either eagerly or lazily trained decision trees. A set of…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…
In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is…