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Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of quantization systems acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description…
Subsampling is a widely used and effective approach for addressing the computational challenges posed by massive datasets. Substantial progress has been made in developing non-uniform, probability-based subsampling schemes that prioritize…
The last couple of years have seen an ever-increasing interest in using different Ising solvers, like Quantum annealers, Coherent Ising machines, and Oscillator-based Ising machines, for solving tough computational problems in various…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the…
Realizing a large-scale quantum computer requires hardware platforms that can simultaneously achieve universality, scalability, and fault tolerance. As a viable pathway to meeting these requirements, quantum computation based on…