Related papers: The infinite Viterbi alignment and decay-convexity
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
Background: Hidden Markov models (HMM) are powerful machine learning tools successfully applied to problems of computational Molecular Biology. In a predictive task, the HMM is endowed with a decoding algorithm in order to assign the most…
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
This paper proposes a globally and exponentially convergent predictive observer for attitude and position estimation based on landmark measurements and velocity (angular and linear) readings. It is assumed that landmark measurements are…
We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…
We study the well-posedness of an infinite-dimensional Hamilton-Jacobi equation posed on the set of non-negative measures and with a monotonic non-linearity. Our results will be used in a companion work to propose a conjecture and prove…
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length…
This paper proposes a computationally tractable algorithm for learning infinite-horizon average-reward linear Markov decision processes (MDPs) and linear mixture MDPs under the Bellman optimality condition. While guaranteeing computational…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant…
In stochastic convex optimization problems, most existing adaptive methods rely on prior knowledge about the diameter bound $D$ when the smoothness or the Lipschitz constant is unknown. This often significantly affects performance as only a…
A relativistic delay model for space very long baseline interferometry (hereafter SVLBI) observation of sources at infinite distance is derived. In SVLBI, where one station is on a spacecraft, the orbiting station's maximum speed in an…
In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain.…
An adaptive algorithm, based on residual type a posteriori indicators of errors measured in $L^{\infty}(L^2)$ and $L^2(L^2)$ norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
Max-convolution is an important problem closely resembling standard convolution; as such, max-convolution occurs frequently across many fields. Here we extend the method with fastest known worst-case runtime, which can be applied to…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…