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VT (Viterbi training), or hard EM, is an efficient way of parameter learning for probabilistic models with hidden variables. Given an observation $y$, it searches for a state of hidden variables $x$ that maximizes $p(x,y \mid \theta)$ by…
Visual place recognition needs to be robust against appearance variability due to natural and man-made causes. Training data collection should thus be an ongoing process to allow continuous appearance changes to be recorded. However, this…
Dynamic structural equation models (DSEMs) combine time-series modeling of within-person processes with hierarchical modeling of between-person differences and differences between timepoints, and have become very popular for the analysis of…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…
To analyze whole-genome genetic data inherited in families, the likelihood is typically obtained from a Hidden Markov Model (HMM) having a state space of 2^n hidden states where n is the number of meioses or edges in the pedigree. There…
Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…
Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…
We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior…
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully…
Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An…
In the competitive landscape of sponsored search, balancing retrieval quality with production latency is a critical challenge. While large retrieval models based on Small Language Models (SLMs) such as Qwen3-Embedding-4B/8B set strong upper…
The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…
The stochastic block model (SBM) is a fundamental tool for community detection in networks, yet the finite-sample performance of inference methods remains underexplored. We evaluate key algorithms-spectral methods, variational inference,…
Time series of conformational dynamics in proteins are usually evaluated with hidden Markov models (HMMs). This approach works well if the number of states and their connectivity is known. However, for the multi-domain protein Hsp90, a…
We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…
Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief…
Deep architecture such as hierarchical semi-Markov models is an important class of models for nested sequential data. Current exact inference schemes either cost cubic time in sequence length, or exponential time in model depth. These costs…