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Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…
Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an…
Software Engineering and the implementation of software has become a challenging task as many tools, frameworks and languages must be orchestrated into one functioning piece. This complexity increases the need for testing and analysis…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
Finetuning can significantly modify the behavior of large language models, including introducing harmful or unsafe behaviors. To study these risks, researchers develop model organisms: models finetuned to exhibit specific known behaviors…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional data-driven methods face challenges in capturing inherently…
Electrospinning is a highly sensitive fabrication process in which small variations in operating parameters can significantly influence fiber morphology and material performance. Machine learning (ML) methods are increasingly employed to…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and…
Sequential recommender systems have achieved steady gains in offline accuracy, yet it remains unclear how close current models are to the intrinsic accuracy limit imposed by the data. A reliable, model-agnostic estimate of this ceiling…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about…