Related papers: Low noise sensitivity analysis of Lq-minimization …
Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that…
Designing robust algorithms capable of training accurate neural networks on uncurated datasets from the web has been the subject of much research as it reduces the need for time consuming human labor. The focus of many previous research…
We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance…
Performance analysis of $l_0$ norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has…
This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
This study surveys the historical development of regularization, tracing its evolution from stepwise regression in the 1960s to recent advancements in formal error control, structured penalties for non-independent features, Bayesian…
Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+\sqrt{epsilon}n. In practical settings, estimation is frequently performed under…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the…
Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these…
Quantization is a critical step to enable efficient LLM serving under limited resource. However, previous research observes that certain weights in the LLM, known as outliers, are significantly sensitive to quantization noises. Existing…
In order to improve the least mean squares (LMS) adaptation algorithm to accommodate the nonlinear transfer function, and to adjust the coefficients of adaptive filter during the actual implement of bias voltage and signal amplitude,…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further…
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
We investigate stable recovery guarantees for phase retrieval under two realistic and challenging noise models: the Poisson model and the heavy-tailed model. Our analysis covers both nonconvex least squares (NCVX-LS) and convex least…
In real-time applications the characteristics and properties of a signal vary inconsistently. So, to maintain the integrity of such signals there is a need for effective adaptive filters. The conventional Least Mean Squared(LMS) algorithm…
We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations…
I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. This connection offers an alternative perspective on…