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Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state…
There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions…
Dropout represents a typical issue to be addressed when dealing with longitudinal studies. If the mechanism leading to missing information is non-ignorable, inference based on the observed data only may be severely biased. A frequent…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a…
Information spread on networks can be efficiently modeled by considering three features: documents' content, time of publication relative to other publications, and position of the spreader in the network. Most previous works model up to…
Lane determination and lane sequence determination are important components for many Connected and Automated Vehicle (CAV) applications. Lane determination has been solved using Hidden Markov Model (HMM) among other methods. The existing…
Most natural language processing systems based on machine learning are not robust to domain shift. For example, a state-of-the-art syntactic dependency parser trained on Wall Street Journal sentences has an absolute drop in performance of…
We show that a language model's ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that…
Diffusion models have demonstrated remarkable capability in generating high-quality visual content from textual descriptions. However, since these models are trained on large-scale internet data, they inevitably learn undesirable concepts,…
The dishonest casino is a well-known hidden Markov model (HMM) often used in education to introduce HMMs and graphical models. A sequence of die rolls is observed with the casino switching between a fair and a loaded die. Instead of…
To improve the routing decisions of individual drivers and the management policies designed by traffic operators, one needs reliable estimates of travel time distributions. Since congestion caused by both recurrent patterns (e.g., rush…
Reasoning over long sequences of observations and actions is essential for many robotic tasks. Yet, learning effective long-context policies from demonstrations remains challenging. As context length increases, training becomes increasingly…
A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…
The prevalence of hidden Markov models (HMMs) in various applications of statistical signal processing and communications is a testament to the power and flexibility of the model. In this paper, we link the identifiability problem with…
Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions…
Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work,…