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Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…
We propose a combined model, which integrates the latent factor model and the logistic regression model, for the citation network. It is noticed that neither a latent factor model nor a logistic regression model alone is sufficient to…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are described by input affine state-space (SS) representations. The conversion approach results in…
Large Language Models (LLMs) have demonstrated strong capabilities across diverse NLP applications, such as translation, text generation, and question answering. Nevertheless, they remain limited in complex settings that demand deep…
We consider the problem of estimating self-exciting generalized linear models from limited binary observations, where the history of the process serves as the covariate. We analyze the performance of two classes of estimators, namely the…
For a sequence $\gamma=(\gamma_n)_{n\ge 1}$, define \[ L_\gamma(z):=\sum_{n\ge 1}\gamma_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}\gamma_d\Bigr)z^n. \] We prove a short rigidity theorem: if $\gamma$ is eventually linearly…
Large language models (LLMs) have demonstrated impressive capabilities in natural language generation. However, their output quality can be inconsistent, posing challenges for generating natural language from logical forms (LFs). This task…
This article considers to model large-dimensional matrix time series by introducing a regression term to the matrix factor model. This is an extension of classic matrix factor model to incorporate the information of known factors or useful…
As machine learning becomes increasingly integral to autonomous decision-making processes involving human interaction, the necessity of comprehending the model's outputs through conversational means increases. Most recently, foundation…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
In comparison to the interpretation of classification models, the explanation of sequence generation models is also an important problem, however it has seen little attention. In this work, we study model-agnostic explanations of a…
Large Language Models (LLMs) have achieved strong performance across a wide range of natural language processing tasks in recent years, including machine translation, text generation, and question answering. As their applications extend to…
Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The…
We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
Table reasoning, a task to answer questions by reasoning over data presented in tables, is an important topic due to the prevalence of knowledge stored in tabular formats. Recent solutions use Large Language Models (LLMs), exploiting the…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
Causal reasoning is a core component of intelligence. Large language models (LLMs) have shown impressive capabilities in generating human-like text, raising questions about whether their responses reflect true understanding or statistical…