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This study introduces an integrated framework for predictive causal inference designed to overcome limitations inherent in conventional single model approaches. Specifically, we combine a Hidden Markov Model (HMM) for spatial health state…

Diffusion models have seen immense success in modelling continuous data across a range of domains such as vision and audio. Despite the challenges of adapting diffusion models to discrete data, recent work explores their application to text…

Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a…

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…

In this work, we analyze the conditions under which information about the context of an input $X$ can improve the predictions of deep learning models in new domains. Following work in marginal transfer learning in Domain Generalization…

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…

Images generated by diffusion models like Stable Diffusion are increasingly widespread. Recent works and even lawsuits have shown that these models are prone to replicating their training data, unbeknownst to the user. In this paper, we…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

In medicine, comorbidities refer to the presence of multiple, co-occurring diseases. Due to their co-occurring nature, the course of one comorbidity is often highly dependent on the course of the other disease and, hence, treatments can…

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to…

Conditional diffusion models have exhibited superior performance in high-fidelity text-guided visual generation and editing. Nevertheless, prevailing text-guided visual diffusion models primarily focus on incorporating text-visual…

A crucial aspect of a rumor detection model is its ability to generalize, particularly its ability to detect emerging, previously unknown rumors. Past research has indicated that content-based (i.e., using solely source posts as input)…

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

Latent topic models have been successfully applied as an unsupervised topic discovery technique in large document collections. With the proliferation of hypertext document collection such as the Internet, there has also been great interest…

Hidden Markov models (HMMs) have been used increasingly to understand how movement patterns of animals arise from behavioural states. An animal is assumed to transition between behavioural states through time, as described by transition…

We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…

Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…

Variable order sequence modeling is an important problem in artificial and natural intelligence. While overcomplete Hidden Markov Models (HMMs), in theory, have the capacity to represent long-term temporal structure, they often fail to…