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Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection sampling, and although it has been used in practice for…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
One of the central problems in the classification of individual test sequences (e.g. genetic analysis), is that of checking for the similarity of sample test sequences as compared with a set of much longer training sequences. This is done…
For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…
Despite the pervasiveness of ordinal labels in supervised learning, it remains common practice in deep learning to treat such problems as categorical classification using the categorical cross entropy loss. Recent methods attempting to…
Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a…
Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In…
Learning with neural networks relies on the complexity of the representable functions, but more importantly, the particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a…
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…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Ranking data arises in a wide variety of application areas but remains difficult to model, learn from, and predict. Datasets often exhibit multimodality, intransitivity, or incomplete rankings---particularly when generated by humans---yet…
The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain…
The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present…
Determining the most appropriate features for machine learning predictive models is challenging regarding performance and feature acquisition costs. In particular, global feature choice is limited given that some features will only benefit…
The rank aggregation problem has received significant recent attention within the computer science community. Its applications today range far beyond the original aim of building metasearch engines to problems in machine learning,…