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We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
State of the art machine learning algorithms are highly optimized to provide the optimal prediction possible, naturally resulting in complex models. While these models often outperform simpler more interpretable models by order of…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
The objective of this article is to study the asymptotic behavior of a new particle filtering approach in the context of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into…
I review the construction of Simplified Models for Dark Matter searches. After discussing the philosophy and some simple examples, I turn the attention to the aspect of the theoretical consistency and to the implications of the necessary…
Markov networks are widely used in many Machine Learning applications including natural language processing, computer vision, and bioinformatics . Learning Markov networks have many complications ranging from intractable computations…
Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there…
Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We…
This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric…
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
When learning a hidden Markov model (HMM), sequen- tial observations can often be complemented by real-valued summary response variables generated from the path of hid- den states. Such settings arise in numerous domains, includ- ing many…
Artificial neural networks are often very complex and too deep for a human to understand. As a result, they are usually referred to as black boxes. For a lot of real-world problems, the underlying pattern itself is very complicated, such…
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of…
Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…
In this lectures given at the Morning side center of Mathematics in October 2016, we present in a very simple framework Hilbertian hypocoercive methods in the case of 1d kinetic inhomogeneous equations, and some illustrations concerning…
We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then…
We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain.…