Multi-horizon time series forecasting has many practical applications such as demand forecasting. Accurate demand prediction is critical to help make buying and inventory decisions for supply chain management of e-commerce and physical retailers, and such predictions are typically required for future horizons extending tens of weeks. This is especially challenging during high-stake sales events when demand peaks are particularly difficult to predict accurately. However, these events are important not only for managing supply chain operations but also for ensuring a seamless shopping experience for customers. To address this challenge, we propose Temporal-Aligned Transformer (TAT), a multi-horizon forecaster leveraging apriori-known context variables such as holiday and promotion events information for improving predictive performance. Our model consists of an encoder and decoder, both embedded with a novel Temporal Alignment Attention (TAA), designed to learn context-dependent alignment for peak demand forecasting. We conduct extensive empirical analysis on two large-scale proprietary datasets from a large e-commerce retailer. We demonstrate that TAT brings up to 30% accuracy improvement on peak demand forecasting while maintaining competitive overall performance compared to other state-of-the-art methods.

Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area which uses randomness to develop improved algorithms for ubiquitous matrix problems. The area has reached a certain level of maturity; but recent hardware trends, efforts to incorporate RandNLA algorithms into core numerical libraries, and advances in machine learning, statistics, and random matrix theory, have lead to new theoretical and practical challenges. This article provides a self-contained overview of RandNLA, in light of these developments.

Selecting suitable architecture parameters and training hyperparameters is essential for enhancing machine learning (ML) model performance. Several recent empirical studies conduct large-scale correlational analysis on neural networks (NNs) to search for effective generalization metrics that can guide this type of model selection. Effective metrics are typically expected to correlate strongly with test performance. In this paper, we expand on prior analyses by examining generalization-metric-based model selection with the following objectives: (i) focusing on natural language processing (NLP) tasks, as prior work primarily concentrates on computer vision (CV) tasks; (ii) considering metrics that directly predict test error instead of the generalization gap; (iii) exploring metrics that do not need access to data to compute. From these objectives, we are able to provide the first model selection results on large pretrained Transformers from Huggingface using generalization metrics. Our analyses consider (I) hundreds of Transformers trained in different settings, in which we systematically vary the amount of data, the model size and the optimization hyperparameters, (II) a total of 51 pretrained Transformers from eight families of Huggingface NLP models, including GPT2, BERT, etc., and (III) a total of 28 existing and novel generalization metrics. Despite their niche status, we find that metrics derived from the heavy-tail (HT) perspective are particularly useful in NLP tasks, exhibiting stronger correlations than other, more popular metrics. To further examine these metrics, we extend prior formulations relying on power law (PL) spectral distributions to exponential (EXP) and exponentially-truncated power law (E-TPL) families.

Federated learning (FL) is a promising way to use the computing power of mobile devices while maintaining the privacy of users. Current work in FL, however, makes the unrealistic assumption that the users have ground-truth labels on their devices, while also assuming that the server has neither data nor labels. In this work, we consider the more realistic scenario where the users have only unlabeled data, while the server has some labeled data, and where the amount of labeled data is smaller than the amount of unlabeled data. We call this learning problem semi-supervised federated learning (SSFL). For SSFL, we demonstrate that a critical issue that affects the test accuracy is the large gradient diversity of the models from different users. Based on this, we investigate several design choices. First, we find that the so-called consistency regularization loss (CRL), which is widely used in semi-supervised learning, performs reasonably well but has large gradient diversity. Second, we find that Batch Normalization (BN) increases gradient diversity. Replacing BN with the recently-proposed Group Normalization (GN) can reduce gradient diversity and improve test accuracy. Third, we show that CRL combined with GN still has a large gradient diversity when the number of users is large. Based on these results, we propose a novel grouping-based model averaging method to replace the FedAvg averaging method. Overall, our grouping-based averaging, combined with GN and CRL, achieves better test accuracy than not just a contemporary paper on SSFL in the same settings (>10%), but also four supervised FL algorithms.

In this paper, we consider hybrid parallelism---a paradigm that employs both Data Parallelism (DP) and Model Parallelism (MP)---to scale distributed training of large recommendation models. We propose a compression framework called Dynamic Communication Thresholding (DCT) for communication-efficient hybrid training. DCT filters the entities to be communicated across the network through a simple hard-thresholding function, allowing only the most relevant information to pass through. For communication efficient DP, DCT compresses the parameter gradients sent to the parameter server during model synchronization. The threshold is updated only once every few thousand iterations to reduce the computational overhead of compression. For communication efficient MP, DCT incorporates a novel technique to compress the activations and gradients sent across the network during the forward and backward propagation, respectively. This is done by identifying and updating only the most relevant neurons of the neural network for each training sample in the data. We evaluate DCT on publicly available natural language processing and recommender models and datasets, as well as recommendation systems used in production at Facebook. DCT reduces communication by at least 100x and 20x during DP and MP, respectively. The algorithm has been deployed in production, and it improves end-to-end training time for a state-of-the-art industrial recommender model by 37%, without any loss in performance.

The ubiquity of deep neural networks (DNNs), cloud-based training, and transfer learning is giving rise to a new cybersecurity frontier in which unsecure DNNs have 'structural malware' (i.e., compromised weights and activation pathways).In particular, DNNs can be designed to have backdoors that allow an adversary to easily and reliably fool an image classifier by adding a pattern of pixels called a trigger.It is generally difficult to detect backdoors, and existing detection methods are computationally expensive and require extensive resources (e.g., access to the training data).Here, we propose a rapid feature-generation technique that quantifies the robustness of a DNN, 'fingerprints' its nonlinearity, and allows us to detect backdoors (if present).Our approach involves studying how a DNN responds to noise-infused images with varying noise intensity, which we summarize with titration curves.We find that DNNs with backdoors are more sensitive to input noise and respond in a characteristic way that reveals the backdoor and where it leads (its 'target').Our empirical results demonstrate that we can accurately detect backdoors with high confidence orders-of-magnitude faster than existing approaches (seconds versus hours).

Motivated by recent developments in serverless systems for large-scale computation as well as improvements in scalable randomized matrix algorithms, we develop OverSketched Newton, a randomized Hessian-based optimization algorithm to solve large-scale convex optimization problems in serverless systems. OverSketched Newton leverages matrix sketching ideas from Randomized Numerical Linear Algebra to compute the Hessian approximately. These sketching methods lead to inbuilt resiliency against stragglers that are a characteristic of serverless architectures. Depending on whether or not the problem is strongly convex, we propose different iteration updates using the approximate Hessian. For both cases, we establish convergence guarantees for OverSketched Newton, and we empirically validate our results by solving large-scale supervised learning problems on real-world datasets. Experiments demonstrate a reduction of ~50% in total running time on AWS Lambda, compared to state-of-the-art distributed optimization schemes.

We present PYHESSIAN, a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks. PYHESSIAN enables fast computations of the top Hessian eigenvalues, the Hessian trace, and the full Hessian eigenvalue/spectral density; it supports distributed-memory execution on cloud/supercomputer systems; and it is available as open source [1]. This general framework can be used to analyze neural network models, including the topology of the loss landscape (i.e., curvature information) to gain insight into the behavior of different models/optimizers. As an example, we analyze the effect of residual connections and Batch Normalization layers on the trainability of neural networks. One recent claim, based on simpler first-order analysis, is that residual connections and Batch Normalization make the loss landscape "smoother," thus making it easier for Stochastic Gradient Descent to converge to a good solution. Our second-order analysis, easily enabled by PYHESSIAN, shows new finer-scale insights, demonstrating that while conventional wisdom is sometimes validated, in other cases it is simply incorrect. In particular, we find that Batch Normalization does not necessarily make the loss landscape smoother, especially for shallow networks.

Given two or more Deep Neural Networks (DNNs) with the same or similar architectures, and trained on the same dataset, but trained with different solvers, parameters, hyper-parameters, regularization, etc., can we predict which DNN will have the best test accuracy, and can we do so without peeking at the test data? In this paper, we show how to use a new Theory of Heavy-Tailed Self-Regularization (HT-SR) to answer this. HT-SR suggests, among other things, that modern DNNs exhibit what we call Heavy-Tailed Mechanistic Universality (HT-MU), meaning that the correlations in the layer weight matrices can be fit to a power law (PL) with exponents that lie in common Universality classes from Heavy-Tailed Random Matrix Theory (HT-RMT). From this, we develop a Universal capacity control metric that is a weighted average of PL exponents. Rather than considering small toy NNs, we examine over 50 different, large-scale pre-trained DNNs, ranging over 15 different architectures, trained on ImagetNet, each of which has been reported to have different test accuracies. We show that this new capacity metric correlates very well with the reported test accuracies of these DNNs, looking across each architecture (VGG16/…/VGG19, ResNet10/…/ResNet152, etc.). We also show how to approximate the metric by the more familiar Product Norm capacity measure, as the average of the log Frobenius norm of the layer weight matrices. Our approach requires no changes to the underlying DNN or its loss function, it does not require us to train a model (although it could be used to monitor training), and it does not even require access to the ImageNet data.

While first-order optimization methods, such as SGD are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of hyper-parameters such as learning rate, stagnation at high training errors, and difficulty in escaping flat regions and saddle points. These issues are particularly acute in highly non-convex settings such as those arising in neural networks. Motivated by this, there has been recent interest in second-order methods that aim to alleviate these shortcomings by capturing curvature information. In this paper, we report detailed empirical evaluations of a class of Newton-type methods, namely sub-sampled variants of trust region (TR) and adaptive regularization with cubics (ARC) algorithms, for non-convex ML problems. In doing so, we demonstrate that these methods not only can be computationally competitive with hand-tuned SGD with momentum, obtaining comparable or better generalization performance, but also they are highly robust to hyper-parameter settings. Further, we show that the manner in which these Newton-type methods employ curvature information allows them to seamlessly escape flat regions and saddle points.

There have long been connections between statistical mechanics and neural networks, but in recent decades these connections have withered. However, in light of recent failings of statistical learning theory and stochastic optimization theory to describe, even qualitatively, many properties of production-quality neural network models, researchers have revisited ideas from the statistical mechanics of neural networks. This tutorial will provide an overview of the area; it will go into detail on how connections with random matrix theory and heavy-tailed random matrix theory can lead to a practical phenomenological theory for large-scale deep neural networks; and it will describe future directions.

First order optimization methods, which rely only on gradient information, are commonly used in diverse machine learning (ML) applications, owing to their simplicity of implementations and low per-iteration computational/storage costs. However, they suffer from significant disadvantages; most notably, their performance degrades with increasing problem ill-conditioning. Furthermore, they often involve a large number of hyperparameters, and are notoriously sensitive to parameters such as the step-size. By incorporating additional information from the Hessian, second-order methods, have been shown to be resilient to many such adversarial effects. However, these advantages come at the expense of higher per-iteration costs, which in “big data” regimes, can be computationally prohibitive. In this paper, we show that, contrary to conventional belief, second-order methods, when designed suitably, can be much more efficient than first-order alternatives for large-scale ML applications. In convex settings, we show that variants of classical Newton's method in which the Hessian and/or gradient are randomly subsampled, coupled with efficient GPU implementations, far outperform state of the art implementations of existing techniques in popular ML software packages such as TensorFlow. We show that our proposed methods (i) achieve better generalization errors in significantly lower wall-clock time – orders of magnitude faster, compared to first-order alternatives (in TensorFlow) and, (ii) offers significantly smaller (and easily parameterized) hyperparameter space making our methods highly robust.

Apache Spark is a popular system aimed at the analysis of large data sets, but recent studies have shown that certain computations---in particular, many linear algebra computations that are the basis for solving common machine learning problems---are significantly slower in Spark than when done using libraries written in a high-performance computing framework such as the Message-Passing Interface (MPI).

In this work we propose LASAGNE, a methodology to learn locality and structure aware graph node embeddings in an unsupervised way. In particular, we show that the performance of existing random-walk based approaches depends strongly on the structural properties of the graph, e.g., the size of the graph, whether the graph has a flat or upward-sloping Network Community Profile (NCP), whether the graph is expander-like, whether the classes of interest are more k-core-like or more peripheral, etc. For larger graphs with flat NCPs that are strongly expander-like, existing methods lead to random walks that expand rapidly, touching many dissimilar nodes, thereby leading to lower-quality vector representations that are less useful for downstream tasks. Rather than relying on global random walks or neighbors within fixed hop distances, LASAGNE exploits strongly local Approximate Personalized PageRank stationary distributions to more precisely engineer local information into node embeddings. This leads, in particular, to more meaningful and more useful vector representations of nodes in poorly-structured graphs. We show that LASAGNE leads to significant improvement in downstream multi-label classification for larger graphs with flat NCPs and that it is comparable for smaller graphs with upward-sloping NCPs.

We explore the trade-offs of performing linear algebra using Apache Spark, compared to traditional C and MPI implementations on HPC platforms. Spark is designed for data analytics on cluster computing platforms with access to local disks and is optimized for data-parallel tasks. We examine three widely-used and important matrix factorizations: NMF (for physical plausability), PCA (for its ubiquity) and CX (for data interpretability). We apply these methods to 1.6TB particle physics, 2.2TB and 16TB climate modeling and 1.1TB bioimaging data. The data matrices are tall-and-skinny which enable the algorithms to map conveniently into Spark's data-parallel model. We perform scaling experiments on up to 1600 Cray XC40 nodes, describe the sources of slowdowns, and provide tuning guidance to obtain high performance.

Graph clustering has many important applications in computing, but due to growing sizes of graph, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest. Motivated partly by this, so-called local algorithms for graph clustering have received significant interest due to the fact that they can find good clusters in a graph with work proportional to the size of the cluster rather than that of the entire graph. This feature has proven to be crucial in making such graph clustering and many of its downstream applications efficient in practice. While local clustering algorithms are already faster than traditional algorithms that touch the entire graph, they are sequential and there is an opportunity to make them even more efficient via parallelization. In this paper, we show how to parallelize many of these algorithms in the shared-memory multicore setting, and we analyze the parallel complexity of these algorithms. We present comprehensive experiments on large-scale graphs showing that our parallel algorithms achieve good parallel speedups on a modern multicore machine, thus significantly speeding up the analysis of local graph clusters in the very large-scale setting.

Graph-based learning methods have a variety of names including semi-supervised and transductive learning. They typically use a diffusion to propagate labels from a small set of nodes with known class labels to the remaining nodes of the graph. While popular, these algorithms, when implemented in a straightforward fashion, are extremely sensitive to the details of the graph construction. Here, we provide four procedures to help make them more robust: recognizing implicit regularization in the diffusion, using a scalable push method to evaluate the diffusion, using rank-based rounding, and densifying the graph through a matrix polynomial. We study robustness with respect to the details of graph constructions, errors in node labeling, degree variability, and a variety of other real-world heterogeneities, studying these methods through a precise relationship with mincut problems. For instance, the densification strategy explicitly adds new weighted edges to a sparse graph. We find that this simple densification creates a graph where multiple diffusion methods are robust to several types of errors. This is demonstrated by a study with predicting product categories from an Amazon co-purchasing network.

Although large social and information networks are often thought of as having hierarchical or tree-like structure, this assumption is rarely tested. We have performed a detailed empirical analysis of the tree-like properties of realistic informatics graphs using two very different notions of tree-likeness: Gromov's d-hyperbolicity, which is a notion from geometric group theory that measures how tree-like a graph is in terms of its metric structure, and tree decompositions, tools from structural graph theory which measure how tree-like a graph is in terms of its cut structure. Although realistic informatics graphs often do not have meaningful tree-like structure when viewed with respect to the simplest and most popular metrics, e.g., the value of d or the tree width, we conclude that many such graphs do have meaningful tree-like structure when viewed with respect to more refined metrics, e.g., a size-resolved notion of d or a closer analysis of the tree decompositions. We also show that, although these two rigorous notions of tree-likeness capture very different tree-like structures in worst-case, for realistic informatics graphs they empirically identify surprisingly similar structure. We interpret this tree-like structure in terms of the recently-characterized "nested core-periphery" property of large informatics graphs, and we show that the fast and scalable k-core heuristic can be used to identify this tree-like structure.

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on what may be broadly termed statistical data analysis. In this article, I will address fundamental aspects of this algorithmic-statistical disconnect, with an eye to bridging the gap between these two very different approaches. A concept that lies at the heart of this disconnect is that of statistical regularization, a notion that has to do with how robust is the output of an algorithm to the noise properties of the input data. Although it is nearly completely absent from computer science, which historically has taken the input data as given and modeled algorithms discretely, regularization in one form or another is central to nearly every application domain that applies algorithms to noisy data. By using several case studies, I will illustrate, both theoretically and empirically, the nonobvious fact that approximate computation, in and of itself, can implicitly lead to statistical regularization. This and other recent work suggests that, by exploiting in a more principled way the statistical properties implicit in worst-case algorithms, one can in many cases satisfy the bicriteria of having algorithms that are scalable to very large-scale databases and that also have good inferential or predictive properties.

Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a network cluster as set of nodes with better internal connectivity than external connectivity, and then one applies approximation algorithms or heuristics to extract sets of nodes that are related to the objective function and that look like good communities for the application of interest.In this paper, we explore a range of network community detection methods in order to compare them and to understand their relative performance and the systematic biases in the clusters they identify. We evaluate several common objective functions that are used to formalize the notion of a network community, and we examine several different classes of approximation algorithms that aim to optimize such objective functions. In addition, rather than simply fixing an objective and asking for an approximation to the best cluster of any size, we consider a size-resolved version of the optimization problem. Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.

Principal Components Analysis (PCA) is the predominant linear dimensionality reduction technique, and has been widely applied on datasets in all scientific domains. We consider, both theoretically and empirically, the topic of unsupervised feature selection for PCA, by leveraging algorithms for the so-called Column Subset Selection Problem (CSSP). In words, the CSSP seeks the "best" subset of exactly k columns from an m x n data matrix A, and has been extensively studied in the Numerical Linear Algebra community. We present a novel two-stage algorithm for the CSSP. From a theoretical perspective, for small to moderate values of k, this algorithm significantly improves upon the best previously-existing results [24, 12] for the CSSP. From an empirical perspective, we evaluate this algorithm as an unsupervised feature selection strategy in three application domains of modern statistical data analysis: finance, document-term data, and genetics. We pay particular attention to how this algorithm may be used to select representative or landmark features from an object-feature matrix in an unsupervised manner. In all three application domains, we are able to identify k landmark features, i.e., columns of the data matrix, that capture nearly the same amount of information as does the subspace that is spanned by the top k "eigenfeatures."

A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the "best" possible community - according to the conductance measure - over a wide range of size scales, and we study over 70 large sparse real-world networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large real-world networks than has been appreciated previously.

We consider feature selection for text classification both theoretically and empirically. Our main result is an unsupervised feature selection strategy for which we give worst-case theoretical guarantees on the generalization power of the resultant classification function f with respect to the classification function f obtained when keeping all the features. To the best of our knowledge, this is the first feature selection method with such guarantees. In addition, the analysis leads to insights as to when and why this feature selection strategy will perform well in practice. We then use the TechTC-100, 20-Newsgroups, and Reuters-RCV2 data sets to evaluate empirically the performance of this and two simpler but related feature selection strategies against two commonly-used strategies. Our empirical evaluation shows that the strategy with provable performance guarantees performs well in comparison with other commonly-used feature selection strategies. In addition, it performs better on certain datasets under very aggressive feature selection.

Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different than the others. In this case, the tensor-CUR decomposition approximately expresses the original data tensor in terms of a basis consisting of underlying subtensors that are actual data elements and thus that have natural interpretation in terms ofthe processes generating the data. In order to demonstrate the general applicability of this tensor decomposition, we apply it to problems in two diverse domains of data analysis: hyperspectral medical image analysis and consumer recommendation system analysis. In the hyperspectral data application, the tensor-CUR decomposition is used to compress the data, and we show that classification quality is not substantially reduced even after substantial data compression. In the recommendation system application, the tensor-CUR decomposition is used to reconstruct missing entries in a user-product-product preference tensor, and we show that high quality recommendations can be made on the basis of a small number of basis users and a small number of product-product comparisons from a new user.