Related papers: Inference on a Distribution from Noisy Draws
Machine learning models are routinely used to support decisions that affect individuals -- be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from…
We study the problem of aggregation noisy labels. Usually, it is solved by proposing a stochastic model for the process of generating noisy labels and then estimating the model parameters using the observed noisy labels. A traditional…
If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…
We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose…
How intelligence arises from the brain is a central problem in science. A crucial aspect of intelligence is dealing with uncertainty -- developing good predictions about one's environment, and converting these predictions into decisions.…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…
We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i)…
We provide new results for nonparametric identification, estimation, and inference of causal effects using `proxy controls': observables that are noisy but informative proxies for unobserved confounding factors. Our analysis applies to…