Related papers: Parameter estimation in softmax decision-making mo…

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…

Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing…

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…

In state-of-the-art deep learning for object recognition, SoftMax and Sigmoid functions are most commonly employed as the predictor outputs. Such layers often produce overconfident predictions rather than proper probabilistic scores, which…

The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation…

Opinion dynamics models such as the bounded confidence models (BCMs) describe how a population can reach consensus, fragmentation, or polarization, depending on a few parameters. Connecting such models to real-world data could help…

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential…

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…

Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…

Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…

For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…

Estimating optimal dynamic policies from offline data is a fundamental problem in dynamic decision making. In the context of causal inference, the problem is known as estimating the optimal dynamic treatment regime. Even though there exists…

Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…

We show that a maximum likelihood approach for parameter estimation in agent-based models (ABMs) of opinion dynamics outperforms the typical simulation-based approach. Simulation-based approaches simulate the model repeatedly in search of a…

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

Large language models (LLMs) have made transformed changes for human society. One of the key computation in LLMs is the softmax unit. This operation is important in LLMs because it allows the model to generate a distribution over possible…