Related papers: Fusing Sufficient Dimension Reduction with Neural …

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…

Deep neural networks are increasingly being used in cognitive modeling as a means of deriving representations for complex stimuli such as images. While the predictive power of these networks is high, it is often not clear whether they also…

Recent advancements have scaled neural networks to unprecedented sizes, achieving remarkable performance across a wide range of tasks. However, deploying these large-scale models on resource-constrained devices poses significant challenges…

Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor…

Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…

Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…

We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

The customizable nature of deep learning models have allowed them to be successful predictors in various disciplines. These models are often trained with respect to thousands or millions of instances for complicated problems, but the…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…

We focus on semiparametric regression that has played a central role in statistics, and exploit the powerful learning ability of deep neural networks (DNNs) while enabling statistical inference on parameters of interest that offers…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…

We consider a data-driven newsvendor problem, where one has access to past demand data and the associated feature information. We solve the problem by estimating the target quantile function using a deep neural network (DNN). The remarkable…

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…

Many machine learning problems, especially multi-modal learning problems, have two sets of distinct features (e.g., image and text features in news story classification, or neuroimaging data and neurocognitive data in cognitive science…

Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…

Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…