Total Variability Model Conventionally formulated as generative model over features Assumes that feature vector distribution is a GMM Distribution Free Formulation Follows from asymptotic normality of Baum-Welch statistics Connections to probabilistic PCA, matrix completion Leads to a stochastic subgradient descent based estimation algorithm Conventional Formulation Collection of feature vector...

In this paper we present a statistical model with a nonsymmetric half-plane (NSHP) region of support for twodimensional continuous-valued vector fields. It has the simplicity, efficiency, and ease of use of the well-known hidden Markov model (HMM) and associated Baum-Welch algorithms for time-series and other one-dimensional problems. At the same time, it is able to learn textures on a twodimen...

In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the Baum-Connes map is a split injection for groups satisfying certain geometric conditions.

Topological maps provide a useful abstraction for robotic navigation and planning. Although stochastic maps can theoretically be learned using the Baum-Welch algorithm, without strong prior constraint on the structure of the model it is slow to converge, requires a great deal of data, and is often stuck in local minima. In this paper, we consider a special case of hidden Markov models for robot...

Continuous-state hidden Markov models (CS-HMMs) are developed as a tool for signal classification. Analogs of the Baum, Viterbi, and Baum–Welch algorithms are formulated for this class of models. The CS-HMM algorithms are then specialized to hidden Gauss–Markov models (HGMMs) with linear Gaussian state-transition and output densities. A new Gaussian refactorization lemma is used to show that th...

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C∗ -algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the re...

The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism μ : K•(BG)→ K•(C ∗ redG) for our class of manifolds, and then classify μ in terms of the ideals in the ring of integers of a quadratic number field K. Next, ...

The predominant learning strategy for H(S)MMs is local search heuristics, of which the Baum-Welch/ expectation maximization (EM) algorithm is mostly used. It is an iterative learning procedure starting with a predefined topology and randomly-chosen initial parameters. However, state-of-the-art approaches based on arbitrarily defined state numbers and parameters can cause the risk of falling int...

A doctor has a duty to give his patient what he believes to be the best treatment. An ethical prerequisite of recommending her to enter a randomised clinical trial (RCT), in which his patient will be randomly allotted to one of two or more treatments, is, as Michael Baum in his chapter stresses, that he is ignorant about their relative efficacy and, hence, justifiably indifferent as to which sh...