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We discuss the role computational algebraic geometry and symbolic computation has played in regards to statistical problems related to inferring phylogenetic networks with a focus on identifiability. This article is an accompanying extended abstract of ...

Personalized learner modeling using cognitive diagnosis (CD), which aims to model learners' cognitive states by diagnosing learner traits from behavioral data, is a fundamental yet significant task in many web learning services. Existing cognitive ...

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical approach may ...

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial ...

Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are unknown) is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we derive ...

Including pairwise or higher-order interactions among predictors of a Generalized Additive Model (GAM) is gaining increasing attention in the literature. However, existing models face anidentifiability challenge. In this paper, we propose pureGAM, an ...

The purpose of this article is to present some recent applications of computer algebra to answer structural and numerical questions in applied sciences. A first example concerns identifiability which is a pre-condition for safely running parameter ...

Linear parameter varying (LPV) models are being increasingly used as a bridge between linear and nonlinear models. From a mathematical point of view, a large class of nonlinear models can be rewritten in LPV or quasi-LPV forms easing their ...

Machine learning (ML) systems often exhibit unexpectedly poor behavior when they are deployed in real-world domains. We identify underspecification in ML pipelines as a key reason for these failures. An ML pipeline is the full procedure followed to train ...

Nonnegative matrix factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in nonunique solutions. Often, there exist a set of feasible solutions (SFS), ...

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series $I(t)$ during the entire epidemic, the parameters can be successfully ...

This paper endeavors to explain how and why self-presentation can affect in-game purchase behavior in Fortnite. As one of the most popular battle royale games in the world, Fortnite employs a free-to-play business model but enjoys a high revenue by ...

We study the following structure learning problem for H-colorings. For a fixed (and known) constraint graph H with q colors, given access to uniformly random H-colorings of an unknown graph G=(V,E), how many samples are required to learn the edges of G? ...

This paper considers a new identifiability condition for additive noise models (ANMs) in which each variable is determined by an arbitrary Borel measurable function of its parents plus an independent error. It has been shown that ANMs are fully ...

We consider the problem of telling apart cause from effect between two univariate continuous-valued random variables X and Y. In general, it is impossible to make definite statements about causality without making assumptions on the underlying model; ...

Applications of Gröbner basis theory to various problems of statistics arises in early 1990s. One of the first works in this field, a computational algebraic statistics, is given by Pistone and Wynn \citePistone-Wynn-1996, where the Gröbner basis theory ...

This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate ...

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry, and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a matrix which ...

In many areas of data mining, data is collected from human beings. In this contribution, we ask the question of how people actually respond to ordinal scales. The main problem observed is that users tend to be volatile in their choices, i.e. complex ...

We used the model of prospective memory and habit development to derive recommendations for designing behavior-change campaigns that used prompts or household visits as reminders. We followed an exemplary procedure comprising the calibration of the ...