Related papers: Fused LASSO as Non-Crossing Quantile Regression
Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into…
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…
The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function $\rho$. We then focus on the special cases when either $\rho$ is the square loss function (for…
The aim of this thesis is to extend the applications of the Quantile Regression Forest (QRF) algorithm to handle mixed-frequency and longitudinal data. To this end, standard statistical approaches have been exploited to build two novel…
A novel approach to quantile estimation in multivariate linear regression models with change-points is proposed: the change-point detection and the model estimation are both performed automatically, by adopting either the quantile fused…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…
Several studies have focused on the Realized Range Volatility, an estimator of the quadratic variation of financial prices, taking into account the impact of microstructure noise and jumps. However, none has considered direct modeling and…
Imbalanced and small data regimes are pervasive in domains such as rare disease imaging, genomics, and disaster response, where labeled samples are scarce and naive augmentation often introduces artifacts. Existing solutions such as…
A new method is proposed to perform joint analysis of longitudinal and cross-sectional growth data. Clustering is first performed to group similar subjects in cross-sectional data to form a pseudo longitudinal data set, then the pseudo…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
Censored quantile regression has emerged as a prominent alternative to classical Cox's proportional hazards model or accelerated failure time model in both theoretical and applied statistics. While quantile regression has been extensively…
We develop a novel "decouple-recouple" dynamic predictive strategy and contribute to the literature on forecasting and economic decision making in a data-rich environment. Under this framework, clusters of predictors generate different…