Related papers: Computing all identifiable functions of parameters…

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…

The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…

Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain…

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…

Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must…

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know…

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference…

Determining the number of factors in high-dimensional factor models remains a fundamental challenge, particularly when data are incomplete. This paper introduces the concept of identifiable factors, those that can be reliably recovered…

Prediction algorithms assign numbers to individuals that are popularly understood as individual "probabilities" -- what is the probability of 5-year survival after cancer diagnosis? -- and which increasingly form the basis for life-altering…

Out-of-distribution (OoD) detection for data-based programs is a goal of paramount importance. Common approaches in the literature tend to train detectors requiring inside-of-distribution (in-distribution, or IoD) and OoD validation…

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of partial differential equations remains limited. We present…

Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability…

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…