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Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…

Attribution methods assess the contribution of inputs to the model prediction. One way to do so is erasure: a subset of inputs is considered irrelevant if it can be removed without affecting the prediction. Though conceptually simple,…

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…

Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…

The linear-in-means model is the standard empirical model of peer effects. Using choice data and exogenous group variation, we first develop a revealed preference style test for the linear-in-means model. This test is formulated as a linear…

The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…

A Profile Mixture Model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend in part on different amino acid…

The predominant way of modelling mortality rates is the Lee-Carter model and its many extensions. The Lee-Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that…

For mathematical and experimental ease, models with time varying parameters are often simplified to assume constant parameters. However, this simplification can potentially lead to identifiability issues (lack of uniqueness of parameter…

Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Identifiability of statistical models is a key notion in unsupervised representation learning. Recent work of nonlinear independent component analysis (ICA) employs auxiliary data and has established identifiable conditions. This paper…

The research paper addresses linear decomposition of time series of non-additive metrics that allows for the identification and interpretation of contributing factors (input features) of variance. Non-additive metrics, such as ratios, are…

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…

Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider…

Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values…

The predominance of machine learning models in many spheres of human activity has led to a growing demand for their transparency. The transparency of models makes it possible to discern some factors, such as security or non-discrimination.…