Related papers: Unexpected properties of bandwidth choice when smo…
Massive data bring the big challenges of memory and computation for analysis. These challenges can be tackled by taking subsamples from the full data as a surrogate. For functional data, it is common to collect multiple measurements over…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
Yes. SE data can have "smoother" boundaries between classes (compared to traditional AI data sets). To be more precise, the magnitude of the second derivative of the loss function found in SE data is typically much smaller. A new…
Generating confidence calibrated outputs is of utmost importance for the applications of deep neural networks in safety-critical decision-making systems. The output of a neural network is a probability distribution where the scores are…
Soft augmentation regularizes the supervised learning process of image classifiers by reducing label confidence of a training sample based on the magnitude of random-crop augmentation applied to it. This paper extends this adaptive label…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
This paper concerns the use of objectness measures to improve the calibration performance of Convolutional Neural Networks (CNNs). CNNs have proven to be very good classifiers and generally localize objects well; however, the loss functions…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
We derive optimal rates of convergence in the supremum norm for estimating the H\"older-smooth mean function of a stochastic process which is repeatedly and discretely observed with additional errors at fixed, multivariate, synchronous…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…
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…
Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one…
Synthetic data is becoming increasingly integral in data-scarce fields such as medical imaging, serving as a substitute for real data. However, its inherent statistical characteristics can significantly impact downstream tasks, potentially…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…