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Generative systems are becoming a crucial part of current design practice. There exist gaps however, between the digital processes, field data and designer's input. To solve this problem, multiple processes were developed in order to…
To evaluate a fitting of a statistical model to given data, calculating a conditional $p$ value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent,…
We answer the question which conjunctive queries are uniquely characterized by polynomially many positive and negative examples, and how to construct such examples efficiently. As a consequence, we obtain a new efficient exact learning…
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…
Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent…
The success of Graph Neural Networks (GNNs) has led to a need for understanding their decision-making process and providing explanations for their predictions, which has given rise to explainable AI (XAI) that offers transparent…
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a…
We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also…
Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…
This note computes a Gr\"obner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gr\"obner basis for unions of schemes given by northwest rank conditions on the space of all matrices of a fixed size.…
We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
The optimization of geometries for aerodynamic design often relies on a large number of expensive simulations to evaluate and iteratively improve the geometries. It is possible to reduce the number of simulations by providing a starting…
Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are…
This paper develops an econometric framework and tools for the identification and inference of a structural parameter in general bunching designs. We present point and partial identification results, which generalize previous approaches in…
We focus in this paper on generating models of quantified first-order formulas over built-in theories, which is paramount in software verification and bug finding. While standard methods are either geared toward proving the absence of…
In this paper a new approach is derived in the context of shape theory. The implemented methodology is motivated in an open problem proposed in \citet{GM93} about the construction of certain shape density involving Euler hypergeometric…