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This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…
Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…
The accuracy of machine learning systems is a widely studied research topic. Established techniques such as cross-validation predict the accuracy on unseen data of the classifier produced by applying a given learning method to a given…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Machine learning (ML) solutions are prevalent in many applications. However, many challenges exist in making these solutions business-grade. For instance, maintaining the error rate of the underlying ML models at an acceptably low level.…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…
Scientific imaging often involves long acquisition times to obtain high-quality data, especially when probing complex, heterogeneous systems. However, reducing acquisition time to increase throughput inevitably introduces significant noise…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
This paper introduces a Fault Diagnosis (Detection, Isolation, and Estimation) method using Set-Membership Estimation (SME) designed for a class of nonlinear systems that are linear to the fault parameters. The methodology advances fault…
Marginalising out uncertain quantities within the internal representations or parameters of neural networks is of central importance for a wide range of learning techniques, such as empirical, variational or full Bayesian methods. We set…