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For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable…
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…
A distinctive representation of image patches in form of features is a key component of many computer vision and robotics tasks, such as image matching, image retrieval, and visual localization. State-of-the-art descriptors, from…
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
In this paper, a Lie group-based neural network method is proposed for solving initial value problems of non linear dynamics. Due to its single-layer structure (MLP), the approach is substantially cheaper than the multilayer perceptron…
In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as SGD. A relaxation of the IID…
Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
The definition of a Neural Network architecture is one of the most critical and challenging tasks to perform. In this paper, we propose ParallelMLPs. ParallelMLPs is a procedure to enable the training of several independent Multilayer…
In this paper, we propose a probabilistic representation of MultiLayer Perceptrons (MLPs) to improve the information-theoretic interpretability. Above all, we demonstrate that the activations being i.i.d. is not valid for all the hidden…
Multilayer perceptrons (MLP) with one hidden layer have been used for a long time to deal with non-linear regression. However, in some task, MLP's are too powerful models and a small mean square error (MSE) may be more due to overfitting…
All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal…
Several machine learning methods aim to learn or reason about complex physical systems. A common first-step towards reasoning is to infer system parameters from observations of its behavior. In this paper, we investigate the performance of…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…