We study the prediction of the accuracy of a neural network given only its weights with the goal of better understanding network training and performance. To do so, we propose a formal setting which frames this task and connects to previous work in this area. We collect (and release) a large dataset of almost 80k convolutional neural networks trained on four image datasets. We demonstrate that strong predictors of accuracy exist. Moreover, they can achieve good predictions while only using simple statistics of the weights. Surprisingly, these predictors are able to rank networks trained on unobserved datasets or using different architectures.

We consider the problem of optimizing an objective function with and without convexity in a simulation-optimization context, where only stochastic zeroth-order information is available. We consider two techniques for estimating gradient/Hessian, namely simultaneous perturbation (SP) and Gaussian smoothing (GS). We introduce an optimization oracle to capture a setting where the function measurements have an estimation error that can be controlled. Our oracle is appealing in several practical contexts where the objective has to be estimated from i.i.d. samples, and increasing the number of samples reduces the estimation error. In the stochastic non-convex optimization context, we analyze the zeroth-order variant of the randomized stochastic gradient (RSG) and quasi-Newton (RSQN) algorithms with a biased gradient/Hessian oracle, and with its variant involving an estimation error component. In particular, we provide non-asymptotic bounds on the performance of both algorithms, and our results provide a guideline for choosing the batch size for estimation, so that the overall error bound matches with the one obtained when there is no estimation error. Next, in the stochastic convex optimization setting, we provide non-asymptotic bounds that hold in expectation for the last iterate of a stochastic gradient descent (SGD) algorithm, and our bound for the GS variant of SGD matches the bound for SGD with unbiased gradient information. We perform simulation experiments on synthetic as well as real-world datasets, and the empirical results validate the theoretical findings.

Many classification problems focus on maximizing the performance only on the samples with the highest relevance instead of all samples. As an example, we can mention ranking problems, accuracy at the top or search engines where only the top few queries matter. In our previous work, we derived a general framework including several classes of these linear classification problems. In this paper, we extend the framework to nonlinear classifiers. Utilizing a similarity to SVM, we dualize the problems, add kernels and propose a componentwise dual ascent method. This allows us to perform one iteration in less than 20 milliseconds on relatively large datasets such as FashionMNIST.

Neural networks are important tools for data-intensive analysis and are commonly applied to model non-linear relationships between dependent and independent variables. However, neural networks are usually seen as "black boxes" that offer minimal information about how the input variables are used to predict the response in a fitted model. This article describes the \pkg{NeuralSens} package that can be used to perform sensitivity analysis of neural networks using the partial derivatives method. Functions in the package can be used to obtain the sensitivities of the output with respect to the input variables, evaluate variable importance based on sensitivity measures and characterize relationships between input and output variables. Methods to calculate sensitivities are provided for objects from common neural network packages in \proglang{R}, including \pkg{neuralnet}, \pkg{nnet}, \pkg{RSNNS}, \pkg{h2o}, \pkg{neural}, \pkg{forecast} and \pkg{caret}. The article presents an overview of the techniques for obtaining information from neural network models, a theoretical foundation of how are calculated the partial derivatives of the output with respect to the inputs of a multi-layer perceptron model, a description of the package structure and functions, and applied examples to compare \pkg{NeuralSens} functions with analogous functions from other available \proglang{R} packages.

Particulate matter pollution is one of the deadliest types of air pollution worldwide due to its significant impacts on the global environment and human health. Particulate Matter (PM2.5) is one of the important particulate pollutants to measure the Air Quality Index (AQI). The conventional instruments used by the air quality monitoring stations to monitor PM2.5 are costly, bulkier, time-consuming, and power-hungry. Furthermore, due to limited data availability and non-scalability, these stations cannot provide high spatial and temporal resolution in real-time. To overcome the disadvantages of existing methodology this article presents analytical equations based prediction approach for PM2.5 using an Artificial Neural Network (ANN). Since the derived analytical equations for the prediction can be computed using a Wireless Sensor Node (WSN) or low-cost processing tool, it demonstrates the usefulness of the proposed approach. Moreover, the study related to correlation among the PM2.5 and other pollutants is performed to select the appropriate predictors. The large authenticate data set of Central Pollution Control Board (CPCB) online station, India is used for the proposed approach. The RMSE and coefficient of determination (R2) obtained for the proposed prediction approach using eight predictors are 1.7973 ug/m3 and 0.9986 respectively. While the proposed approach results show RMSE of 7.5372 ug/m3 and R2 of 0.9708 using three predictors. Therefore, the results demonstrate that the proposed approach is one of the promising approaches for monitoring PM2.5 without power-hungry gas sensors and bulkier analyzers.

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a comprehensive mechanism for computing the least squares estimator of a multivariate shape-constrained convex regression function in $\mathbb{R}^d$. We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points. For solving the generally very large-scale convex QP, we design two efficient algorithms, one is the symmetric Gauss-Seidel based alternating direction method of multipliers ({\tt sGS-ADMM}), and the other is the proximal augmented Lagrangian method ({\tt pALM}) with the subproblems solved by the semismooth Newton method ({\tt SSN}). Comprehensive numerical experiments, including those in the pricing of basket options and estimation of production functions in economics, demonstrate that both of our proposed algorithms outperform the state-of-the-art algorithm. The {\tt pALM} is more efficient than the {\tt sGS-ADMM} but the latter has the advantage of being simpler to implement.

Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a $D$-dimensional space into a set of blocks. In this way, the data points lie in the same block would share certain kinds of homogeneity. BNSP models can be applied to various areas, such as regression/classification trees, random feature construction, relational modeling, etc. In this survey, we investigate the current progress of BNSP research through the following three perspectives: models, which review various strategies for generating the partitions in the space and discuss their theoretical foundation `self-consistency'; applications, which cover the current mainstream usages of BNSP models and their potential future practises; and challenges, which identify the current unsolved problems and valuable future research topics. As there are no comprehensive reviews of BNSP literature before, we hope that this survey can induce further exploration and exploitation on this topic.

Machine learning systems must adapt to data distributions that evolve over time, in applications ranging from sensor networks and self-driving car perception modules to brain-machine interfaces. We consider gradual domain adaptation, where the goal is to adapt an initial classifier trained on a source domain given only unlabeled data that shifts gradually in distribution towards a target domain. We prove the first non-vacuous upper bound on the error of self-training with gradual shifts, under settings where directly adapting to the target domain can result in unbounded error. The theoretical analysis leads to algorithmic insights, highlighting that regularization and label sharpening are essential even when we have infinite data, and suggesting that self-training works particularly well for shifts with small Wasserstein-infinity distance. Leveraging the gradual shift structure leads to higher accuracies on a rotating MNIST dataset and a realistic Portraits dataset.

The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide a simple explanation for this by measuring the bias and variance of neural networks: while the bias is monotonically decreasing as in the classical theory, the variance is unimodal or bell-shaped: it increases then decreases with the width of the network. We vary the network architecture, loss function, and choice of dataset and confirm that variance unimodality occurs robustly for all models we considered. The risk curve is the sum of the bias and variance curves and displays different qualitative shapes depending on the relative scale of bias and variance, with the double descent curve observed in recent literature as a special case. We corroborate these empirical results with a theoretical analysis of two-layer linear networks with random first layer. Finally, evaluation on out-of-distribution data shows that most of the drop in accuracy comes from increased bias while variance increases by a relatively small amount. Moreover, we find that deeper models decrease bias and increase variance for both in-distribution and out-of-distribution data.

Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive study, it is poorly understood whether or not there exist natural algorithms that can provably converge to a local minimum. Part of the reason is because the objective is heavily symmetric and its gradient is not Lipschitz. In this paper we define a multiplicative weight update type dynamics (modification of the seminal Lee-Seung algorithm) that runs concurrently and provably avoids saddle points (first order stationary points that are not second order). Our techniques combine tools from dynamical systems such as stability and exploit the geometry of the NMF objective by reducing the standard NMF formulation over the non-negative orthant to a new formulation over (a scaled) simplex. An important advantage of our method is the use of concurrent updates, which permits implementations in parallel computing environments.