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The latent position model (LPM) is a popular method used in network data analysis where nodes are assumed to be positioned in a $p$-dimensional latent space. The latent shrinkage position model (LSPM) is an extension of the LPM which…
Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their…
The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are…
Learning from label proportions (LLP) is a weakly supervised setting for classification in which unlabeled training instances are grouped into bags, and each bag is annotated with the proportion of each class occurring in that bag. Prior…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are…
Hyperparameters greatly impact models' capabilities; however, modern models are too large for extensive search. Instead, researchers design recipes that train well across scales based on their understanding of the hyperparameters. Despite…
A multilayer perceptron (MLP) is typically made of multiple fully connected layers with nonlinear activation functions. There have been several approaches to make them better (e.g. faster convergence, better convergence limit, etc.). But…
The goal of mechanistic interpretability is discovering simpler, low-rank algorithms implemented by models. While we can compress activations into features, compressing nonlinear feature-maps -- like MLP layers -- is an open problem. In…
This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a Hidden Markov Model (HMM), which is recognized as a fundamental setting to model multiple testing under dependence since the seminal…
We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A…
Linear mixed effects models (LMMs) are a popular and powerful tool for analyzing clustered or repeated observations for numeric outcomes. LMMs consist of a fixed and a random component, specified in the model through their respective design…
We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of…
The performance of land surface models (LSMs) significantly affects the understanding of atmospheric and related processes. Many of the LSMs' soil and vegetation parameters were unknown so that it is crucially important to efficiently…
Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs. Several studies on LLM efficiency optimization argue that it is possible to prune a significant portion…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
In this paper we study the asymptotics (as $n\to \infty$) of the sequences of Laguerre polynomials with varying complex parameters $\alpha$ depending on the degree $n$. More precisely, we assume that $\alpha_n = n A_n, $ and $ \lim_n A_n=A…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…