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Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…

Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…

Long sequences occur in abundance within real-world scenarios, hence properly modelling them opens numerous down-stream use-cases. Deep neural networks, however, have often struggled with these for a variety of reasons. Recent advances,…

We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…

We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…

In recent years, the sequence-to-sequence learning neural networks with attention mechanism have achieved great progress. However, there are still challenges, especially for Neural Machine Translation (NMT), such as lower translation…

Artificial neural networks (ANNs) have achieved significant success in tackling classical and modern machine learning problems. As learning problems grow in scale and complexity, and expand into multi-disciplinary territory, a more modular…

We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…

Sequence labeling (SL) is a fundamental research problem encompassing a variety of tasks, e.g., part-of-speech (POS) tagging, named entity recognition (NER), text chunking, etc. Though prevalent and effective in many downstream applications…

Crime prediction is a widely studied research problem due to its importance in ensuring safety of city dwellers. Starting from statistical and classical machine learning based crime prediction methods, in recent years researchers have…

Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the…

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future…

While sequence-to-sequence (seq2seq) models achieve state-of-the-art performance in many natural language processing tasks, they can be too slow for real-time applications. One performance bottleneck is predicting the most likely next token…

The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification…

Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…

We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…

The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…

Time series data can be subject to changes in the underlying process that generates them and, because of these changes, models built on old samples can become obsolete or perform poorly. In this work, we present a way to incorporate…

Accurate estimation of predictive uncertainty (model calibration) is essential for the safe application of neural networks. Many instances of miscalibration in modern neural networks have been reported, suggesting a trend that newer, more…