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Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good…
Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
As machine learning models grow increasingly competent, their predictions can supplement scarce or expensive data in various important domains. In support of this paradigm, algorithms have emerged to combine a small amount of high-fidelity…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates,…
Quantile regression is a statistical method which, unlike classical regression, aims to predict the conditional quantiles. Classical quantile regression methods face difficulties, particularly when the quantile under consideration is…
Many applications of LLM-based text regression require predicting a full conditional distribution rather than a single point value. We study distributional regression under empirical-quantile supervision, where each input is paired with…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
We design an efficient data structure for computing a suitably defined approximate depth of any query point in the arrangement $\mathcal{A}(S)$ of a collection $S$ of $n$ halfplanes or triangles in the plane or of halfspaces or simplices in…
We consider a simple approach to solving assortment optimization under the random utility maximization model. The approach uses Monte-Carlo simulation to construct a ranking-based choice model that serves as a proxy for the true choice…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…