Related papers: Relative Entropy Estimation in Function Space: The…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which…
A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
Many of the recent trajectory optimization algorithms alternate between linear approximation of the system dynamics around the mean trajectory and conservative policy update. One way of constraining the policy change is by bounding the…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…
Simulation-based inference (SBI) is a statistical inference approach for estimating latent parameters of a physical system when the likelihood is intractable but simulations are available. In practice, SBI is often hindered by model…
Understanding the dynamics of an environment, such as the movement of humans and vehicles, is crucial for agents to achieve long-term autonomy in urban environments. This requires the development of methods to capture the multi-modal and…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
We present a sample path dependent measure of causal influence between time series. The proposed causal measure is a random sequence, a realization of which enables identification of specific patterns that give rise to high levels of causal…
Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The most well-known are the von Neumann entropy $trace (\rho\log \rho)$ and a generalization of the…
In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of 1) a weighted Mean Square Error (wMSE)…
Discriminator Guidance has become a popular method for efficiently refining pre-trained Score-Matching Diffusion models. However, in this paper, we demonstrate that the standard implementation of this technique does not necessarily lead to…
This short note is on a property of the Kullback-Leibler (KL) divergence which indicates that independent Gaussian distributions minimize the KL divergence from given independent Gaussian distributions. The primary purpose of this note is…
This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that…
Accurate trajectory prediction of vehicles is essential for reliable autonomous driving. To maintain consistent performance as a vehicle driving around different cities, it is crucial to adapt to changing traffic circumstances and achieve…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
Predicting individuals' next locations is a core task in human mobility modelling, with wide-ranging implications for urban planning, transportation, public policy and personalised mobility services. Traditional approaches largely depend on…