Related papers: Identification of unknown parameters and predictio…

There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization…

Developing robust inference for models with nonparametric Unobserved Heterogeneity (UH) is both important and challenging. We propose novel Debiased Machine Learning (DML) procedures for valid inference on functionals of UH, allowing for…

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

Nonparametric empirical Bayes methods provide a flexible and attractive approach to high-dimensional data analysis. One particularly elegant empirical Bayes methodology, involving the Kiefer-Wolfowitz nonparametric maximum likelihood…

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…

We aim at the construction of a Hidden Markov Model (HMM) of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback-Leibler divergence rate, a given stationary process. We establish, under…

Trustworthiness in model predictions is crucial for safety-critical applications in the real world. However, deep neural networks often suffer from the issues of uncertainty estimation, such as miscalibration. In this study, we propose…

The primary example of instance-based learning is the $k$-nearest neighbor rule (kNN), praised for its simplicity and the capacity to adapt to new unseen data and toss away old data. The main disadvantages often mentioned are the…

While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state…

Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm…

It often happens that some sensitive personal information, such as credit card numbers or passwords, are mistakenly incorporated in the training of machine learning models and need to be removed afterwards. The removal of such information…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…

Linear models have found widespread use in statistical investigations. For every linear model there exists a matrix representation for which the ReML (Restricted Maximum Likelihood) can be constructed from the elements of the corresponding…

The model of partially observed linear stochastic differential equations depending on some unknown parameters is considered. An proximation of the unobserved component is proposed. This approximation is realized in three steps. First an…

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters…