Related papers: Information and Statistical Efficiency When Quanti…
A popular approach to learning encoders for lossy compression is to use additive uniform noise during training as a differentiable approximation to test-time quantization. We demonstrate that a uniform noise channel can also be implemented…
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…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical…
This paper considers estimation of a random variable in Poisson noise with signal scaling coefficient and dark current as explicit parameters of the noise model. Specifically, the paper focuses on properties of the conditional mean…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always…
In black-box optimization, noise in the objective function is inevitable. Noise disrupts the ranking of candidate solutions in comparison-based optimization, possibly deteriorating the search performance compared with a noiseless scenario.…
The method of stable random projections is a tool for efficiently computing the $l_\alpha$ distances using low memory, where $0<\alpha \leq 2$ is a tuning parameter. The method boils down to a statistical estimation task and various…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
In a typical optimization problem, the task is to pick one of a number of options with the lowest cost or the highest value. In practice, these cost/value quantities often come through processes such as measurement or machine learning,…
Quantum reservoir computing offers a promising approach to the utilization of complex quantum dynamics in machine learning. Statistical noise inevitably arises in real settings of quantum reservoir computing (QRC) due to the practical…
It is important to know noise levels of boson sampling in order to cautiously demonstrate the quantum computational advantage or realize certain tasks. Based on those statistical benchmark methods such as the correlators and clouds, which…
This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…