Related papers: Information and Statistical Efficiency When Quanti…
In this manuscript, a purely data driven statistical regularization method is proposed for extracting the information from big data with randomly distributed noise. Since the variance of the noise maybe large, the method can be regarded as…
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…
Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a…
An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
Quantization is essential for reducing the computational cost and memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes,…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
I calculate the statistics of correlation of two digitized noiselike signals, which are drawn from complex Gaussian distributions, sampled, quantized, correlated, and averaged. Averaged over many such samples, the correlation r approaches a…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation…
We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level, by means of Gaussian probe states. In particular we discuss both unitary and random disturbance, by…
Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still possible. When the…
Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…
Active learning seeks to build the best possible model with a budget of labelled data by sequentially selecting the next point to label. However the training set is no longer \textit{iid}, violating the conditions required by existing…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
Coherent ensembles of $N$ qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. In some contexts, the strength of diffusion may be…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive iid Gaussian noise, where the signal lies in the span of a finite basis. For the…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…