Related papers: Identification in a Fully Nonparametric Transforma…
Latent feature models (LFM)s are widely employed for extracting latent structures of data. While offering high, parameter estimation is difficult with LFMs because of the combinational nature of latent features, and non-identifiability is a…
The purpose of this paper is to present an algorithm for inferring nondeterministic functional transducers. It has a lot in common with other well known algorithms such has RPNI and OSTIA. Indeed we will argue that this algorithm is a…
We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…
This paper examines the nonparametric identifiability of production functions, considering firm heterogeneity beyond Hicks-neutral technology terms. We propose a finite mixture model to account for unobserved heterogeneity in production…
We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation)…
Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
In this paper, we address the problem of identifying linear structural equation models. We first extend the edge set half-trek criterion to cover a broader class of models. We then show that any semi-Markovian linear model can be…
Representation learning models exhibit a surprising stability in their internal representations. Whereas most prior work treats this stability as a single property, we formalize it as two distinct concepts: statistical identifiability…
Regression trees are becoming increasingly popular as omnibus predicting tools and as the basis of numerous modern statistical learning ensembles. Part of their popularity is their ability to create a regression prediction without ever…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output equations is one method for…
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…
Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows…
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…
Binary multirelations can model alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…
Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…