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Recently, the multi-step inertial randomized Kaczmarz (MIRK) method for solving large-scale linear systems was proposed in [17]. In this paper, we incorporate the greedy probability criterion into the MIRK method, along with the introduction of a tighter threshold parameter for this criterion. We prove that the proposed greedy MIRK (GMIRK) method enjoys an improved deterministic linear convergence compared to both the MIRK method and the greedy randomized Kaczmarz method. Furthermore, we exhibit that the multi-step inertial extrapolation approach can be seen geometrically as an orthogonal projection method, and establish its relationship with the sketch-and-project method [15] and the oblique projection technique [22]. Numerical experiments are provided to confirm our results.

Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using kernel and inference methods. Here we build upon this limit and provide a field-theoretic formalism which covers the generalization properties of infinitely wide networks. We systematically compute generalization properties of linear, non-linear, and deep non-linear networks for kernel matrices with heterogeneous entries. In contrast to currently employed spectral methods we derive the generalization properties from the statistical properties of the input, elucidating the interplay of input dimensionality, size of the training data set, and variability of the data. We show that data variability leads to a non-Gaussian action reminiscent of a ($\varphi^3+\varphi^4$)-theory. Using our formalism on a synthetic task and on MNIST we obtain a homogeneous kernel matrix approximation for the learning curve as well as corrections due to data variability which allow the estimation of the generalization properties and exact results for the bounds of the learning curves in the case of infinitely many training data points.

Convolutional neural network (CNN) is an important deep learning method. The convolution operation takes a large proportion of the total execution time for CNN. Feature maps for convolution operation are usually sparse. Multiplications and additions for zero values in the feature map are useless for convolution results. In addition, the convolution layer and pooling layer are computed separately in traditional methods, which leads to frequent data transfer between CPU and GPU. Based on these observations, we propose two new methods to accelerate CNN on GPUs. The first method focuses on accelerating convolution operation and reducing the calculation of zero values. The second method combines the operations of one convolution layer with the following pooling layer to effectively reduce traffic between CPU and GPU. For the first method, we extract some convolution layers from LeNet, AlexNet, and GoogLeNet, and can achieve up to 3.6X speedup over cuDNN for the single-layer convolution on GPU. Experiment on VGG-19 achieves 3.5X speedup over cuDNN for convolution operation on average. For the second method, the experiment on VGG-19 achieves 4.3X speedup over cuDNN on average.

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in extreme value theory. Our work studies the theoretical performance of spectral clustering based on a random $k$-nearest neighbor graph constructed from an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. In particular, we derive the asymptotic distribution of extremes arising from a linear factor model and prove that, under certain conditions, spectral clustering can consistently identify the clusters of extremes arising in this model. Leveraging this result we propose a simple consistent estimation strategy for learning the angular measure. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods.

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear dynamics from measurements. Until now, the situation where for large-scale systems, we (i) only have access to partial observations (i.e., measurements, as is very common for experimental data) or (ii) deliberately perform coarse graining (for efficiency reasons) has not been treated to its full extent. In this paper, we address the pitfall associated with this situation, that the classical EDMD algorithm does not automatically provide a Koopman operator approximation for the underlying system if we do not carefully select the number of observables. Moreover, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to massively increase the model efficiency. We also briefly draw a connection to domain decomposition techniques for partial differential equations and present numerical evidence using the Kuramoto--Sivashinsky equation.

Comparative effectiveness research frequently addresses a time-to-event outcome and can require unique considerations in the presence of treatment noncompliance. Motivated by the challenges in addressing noncompliance in the ADAPTABLE pragmatic trial, we develop a multiply robust estimator to estimate the principal survival causal effects under the principal ignorability and monotonicity assumption. The multiply robust estimator involves several working models including that for the treatment assignment, the compliance strata, censoring, and time-to-event of interest. The proposed estimator is consistent even if one, and sometimes two, of the working models are misspecified. We apply the multiply robust method in the ADAPTABLE trial to evaluate the effect of low- versus high-dose aspirin assignment on patients' death and hospitalization from cardiovascular diseases. We find that, comparing to low-dose assignment, assignment to the high-dose leads to differential effects among always high-dose takers, compliers, and always low-dose takers. Such treatment effect heterogeneity contributes to the null intention-to-treatment effect, and suggests that policy makers should design personalized strategies based on potential compliance patterns to maximize treatment benefits to the entire study population. We further perform a formal sensitivity analysis for investigating the robustness of our causal conclusions under violation of two identification assumptions specific to noncompliance.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.