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This work investigates the framework and performance issues of the composite neural network, which is composed of a collection of pre-trained and non-instantiated neural network models connected as a rooted directed acyclic graph for…
Predicting the number of clock cycles a processor takes to execute a block of assembly instructions in steady state (the throughput) is important for both compiler designers and performance engineers. Building an analytical model to do so…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
The scattering framework offers an optimal hierarchical convolutional decomposition according to its kernels. Convolutional Neural Net (CNN) can be seen as an optimal kernel decomposition, nevertheless it requires large amount of training…
A learning machine, like all machines, is an open system driven far from thermal equilibrium by access to a low entropy source of free energy. We discuss the connection between machines that learn, with low probability of error, and the…
Hyperspectral imagery is rich in spatial and spectral information. Using 3D-CNN can simultaneously acquire features of spatial and spectral dimensions to facilitate classification of features, but hyperspectral image information spectral…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show…
Most existing interpretable methods explain a black-box model in a post-hoc manner, which uses simpler models or data analysis techniques to interpret the predictions after the model is learned. However, they (a) may derive contradictory…
The interpretability of machine learning, particularly for deep neural networks, is crucial for decision making in real-world applications. One approach is replacing the un-interpretable machine learning model with a surrogate model, which…
In machine learning, we are given a dataset of the form $\{(\mathbf{x}_j,y_j)\}_{j=1}^M$, drawn as i.i.d. samples from an unknown probability distribution $\mu$; the marginal distribution for the $\mathbf{x}_j$'s being $\mu^*$. We propose…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…
Most accurate predictions are typically obtained by learning machines with complex feature spaces (as e.g. induced by kernels). Unfortunately, such decision rules are hardly accessible to humans and cannot easily be used to gain insights…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out…
The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems. Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel…