Related papers: Quantized Nonparametric Estimation over Sobolev El…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

Quantum parameter estimation holds the promise of quantum technologies, in which physical parameters can be measured with much greater precision than what is achieved with classical technologies. However, how to obtain a best precision when…

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

The continuous improvements on image compression with variational autoencoders have lead to learned codecs competitive with conventional approaches in terms of rate-distortion efficiency. Nonetheless, taking the quantization into account…

There have been a number of studies on sparse signal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance.…

We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…

We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate-optimal estimator which is adaptive…

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is…

Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit…

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results.…

We consider the problem of the classical simulation of quantum measurements in the scenario of communication complexity. Regev and Toner (2007) have presented a 2-bit protocol which simulates one particular correlation function arising from…

Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…

We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…

Pairwise similarities and dissimilarities between data points might be easier to obtain than fully labeled data in real-world classification problems, e.g., in privacy-aware situations. To handle such pairwise information, an empirical risk…