Related papers: Squared Linear Models
We solve a supersymmetric matrix model with a general potential. While matrix models usually describe surfaces, supersymmetry enforces a cancellation of bosonic and fermionic loops and only diagrams corresponding to so-called branched…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
A (global) determinantal representation of hypersurface in P^n is a matrix, whose entries are linear forms in homogeneous coordinates and whose determinant defines the hypersurface. We study the properties of such representations for…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
The aim of this note is to state a couple of general results about the properties of the penalized maximum likelihood estimators (pMLE) and of the posterior distribution for parametric models in a non-asymptotic setup and for possibly large…
A key object of study in stochastic topology is a random simplicial complex. In this work we study a multi-parameter random simplicial complex model, where the probability of including a $k$-simplex, given the lower dimensional structure,…
[Spreadsheet] Models are invaluable tools for strategic planning. Models help key decision makers develop a shared conceptual understanding of complex decisions, identify sensitivity factors and test management scenarios. Different…
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…
Log-linear models are typically fitted to contingency table data to describe and identify the relationship between different categorical variables. However, the data may include observed zero cell entries. The presence of zero cell entries…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…
This paper estimates the break point for large-dimensional factor models with a single structural break in factor loadings at a common unknown date. First, we propose a quasi-maximum likelihood (QML) estimator of the change point based on…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…