Knowledge graph (KG) completion aims to identify additional facts that can be inferred from the existing facts in the KG. Recent developments in this field have explored this task in the inductive setting, where at test time one sees entities that were not present during training; the most performant models in the inductive setting have employed path encoding modules in addition to standard subgraph encoding modules. This work similarly focuses on KG completion in the inductive setting, without the explicit use of path encodings, which can be time-consuming and introduces several hyperparameters that require costly hyperparameter optimization. Our approach uses a Transformer-based subgraph encoding module only; we introduce connection-biased attention and entity role embeddings into the subgraph encoding module to eliminate the need for an expensive and time-consuming path encoding module. Evaluations on standard inductive KG completion benchmark datasets demonstrate that our Connection-Biased Link Prediction (CBLiP) model has superior performance to models that do not use path information. Compared to models that utilize path information, CBLiP shows competitive or superior performance while being faster. Additionally, to show that the effectiveness of connection-biased attention and entity role embeddings also holds in the transductive setting, we compare CBLiP's performance on the relation prediction task in the transductive setting.

Causality-informed machine learning has been proposed as an avenue for achieving many of the goals of modern machine learning, from ensuring generalization under domain shifts to attaining fairness, robustness, and interpretability. A key component of causal machine learning is the inference of causal structures from observational data; in practice, this data may be incompletely observed. Prior work has demonstrated that adversarial perturbations of completely observed training data may be used to force the learning of inaccurate structural causal models (SCMs). However, when the data can be audited for correctness (e.g., it is cryptographically signed by its source), this adversarial mechanism is invalidated. This work introduces a novel attack methodology wherein the adversary deceptively omits a portion of the true training data to bias the learned causal structures in a desired manner (under strong signed sample input validation, this behavior seems to be the only strategy available to the adversary). Under this model, theoretically sound attack mechanisms are derived for the case of arbitrary SCMs, and a sample-efficient learning-based heuristic is given. Experimental validation of these approaches on real and synthetic datasets, across a range of SCMs from the family of additive noise models (linear Gaussian, linear non-Gaussian, and non-linear Gaussian), demonstrates the effectiveness of adversarial missingness attacks at deceiving popular causal structure learning algorithms.

Learning visual representations with interpretable features, i.e., disentangled representations, remains a challenging problem. Existing methods demonstrate some success but are hard to apply to large-scale vision datasets like ImageNet. In this work, we propose a simple post-processing framework to disentangle content and style in learned representations from pre-trained vision models. We model the pre-trained features probabilistically as linearly entangled combinations of the latent content and style factors and develop a simple disentanglement algorithm based on the probabilistic model. We show that the method provably disentangles content and style features and verify its efficacy empirically. Our post-processed features yield significant domain generalization performance improvements when the distribution shift occurs due to style changes or style-related spurious correlations.

Causality-informed machine learning has been proposed as an avenue for achieving many of the goals of modern machine learning, from ensuring generalization under domain shifts to attaining fairness, robustness, and interpretability. A key component of causal machine learning is the inference of causal structures from observational data; in practice, this data may be incompletely observed. Prior work has demonstrated that adversarial perturbations of completely observed training data may be used to force the learning of inaccurate causal structural models (SCMs). However, when the data can be audited for correctness (e.g., it is cryptographically signed by its source), this adversarial mechanism is invalidated. This work introduces a novel attack methodology wherein the adversary deceptively omits a portion of the true training data to bias the learned causal structures in a desired manner (under strong signed sample input validation, this behavior seems to be the only strategy available to the adversary). Under this model, theoretically sound attack mechanisms are derived for the case of arbitrary SCMs, and a sample-efficient learning-based heuristic is given. Experimental validation of these approaches on real and synthetic data sets demonstrates the effectiveness of adversarial missingness attacks at deceiving popular causal structure learning algorithms.

Threat intelligence on malware attacks and campaigns is increasingly being shared with other security experts for a cost or for free. Other security analysts use this intelligence to inform them of indicators of compromise, attack techniques, and preventative actions. Security analysts prepare threat analysis reports after investigating an attack, an emerging cyber threat, or a recently discovered vulnerability. Collectively known as cyber threat intelligence (CTI), the reports are typically in an unstructured format and, therefore, challenging to integrate seamlessly into existing intrusion detection systems. This paper proposes a framework that uses the aggregated CTI for analysis and defense at scale. The information is extracted and stored in a structured format using knowledge graphs such that the semantics of the threat intelligence can be preserved and shared at scale with other security analysts. Specifically, we propose the first semi-supervised open-source knowledge graph-based framework, TINKER, to capture cyber threat information and its context. Following TINKER, we generate a Cyberthreat Intelligence Knowledge Graph (CTI-KG) and demonstrate the usage using different use cases.

In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least squares regression, low-rank approximation, and the approximation of leverage scores. A key property of sketching matrices is that of subspace embedding. In this paper, we study sketching matrices that are obtained from bipartite graphs that are sparse, i.e., have left degree s that is small. In particular, we explore two popular classes of sparse graphs, namely, expander graphs and magical graphs. For a given subspace ${\mathcal{U}} \subseteq {{\mathbb{R}}^n}$ of dimension k, we show that the magical graph with left degree s = 2 yields a (1 ± ϵ) ℓ2-subspace embedding for ${\mathcal{U}}$, if the number of right vertices (the sketch size) $m = {\mathcal{O}}\left( {{k^2}/{\varepsilon ^2}} \right)$. The expander graph with $s = {\mathcal{O}}(\log k/\varepsilon )$ yields a subspace embedding for $m = {\mathcal{O}}\left( {k\log k/{\varepsilon ^2}} \right)$. We also discuss the construction of sparse sketching matrices with reduced randomness using expanders based on error-correcting codes. Empirical results on various synthetic and real datasets show that these sparse graph sketching matrices work very well in practice.

This work considers the canonical polyadic decomposition (CPD) of tensors using proximally regularized sketched alternating least squares algorithms. First, it establishes a sublinear rate of convergence for proximally regularized sketched CPD algorithms under two natural conditions that are known to be satisfied by many popular forms of sketching. Second, it demonstrates that the iterative nature of CPD algorithms can be exploited algorithmically to choose more performant sketching rates. This is accomplished by introducing CPD-MWU, a proximally-regularized sketched alternating least squares algorithm that adaptively selects the sketching rate at each iteration. On both synthetic and real data we observe that for noisy tensors CPD-MWU produces decompositions of comparable accuracy to the standard CPD decomposition in less time, often half the time; for ill-conditioned tensors, given the same time budget, CPD-MWU produces decompositions with an order-of-magnitude lower relative error. For a representative real-world dataset CPD-MWU produces residual errors on average 20% lower than CPRAND-MIX and 44% lower than SPALS, two recent sketched CPD algorithms.

Summary The Apache Spark framework for distributed computation is popular in the data analytics community due to its ease of use, but its MapReduce‐style programming model can incur significant overheads when performing computations that do not map directly onto this model. One way to mitigate these costs is to off‐load computations onto MPI codes. In recent work, we introduced Alchemist, a system for the analysis of large‐scale data sets. Alchemist calls MPI‐based libraries from within Spark applications, and it has minimal coding, communication, and memory overheads. In particular, Alchemist allows users to retain the productivity benefits of working within the Spark software ecosystem without sacrificing performance efficiency in linear algebra, machine learning, and other related computations. In this paper, we discuss the motivation behind the development of Alchemist, and we provide a detailed overview of its design and usage. We also demonstrate the efficiency of our approach on medium‐to‐large data sets, using some standard linear algebra operations, namely, matrix multiplication and the truncated singular value decomposition of a dense matrix, and we compare the performance of Spark with that of Spark+Alchemist. These computations are run on the NERSC supercomputer Cori Phase 1, a Cray XC40.

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel approximation, e.g., the Nystrom method, has been applied in previous works to approximately solve kernel learning problems when both of the above conditions are present. This work analyzes the application of this paradigm to kernel $k$-means clustering, and shows that applying the linear $k$-means clustering algorithm to $\frac{k}{\epsilon} (1 + o(1))$ features constructed using a so-called rank-restricted Nystrom approximation results in cluster assignments that satisfy a $1 + \epsilon$ approximation ratio in terms of the kernel $k$-means cost function, relative to the guarantee provided by the same algorithm without the use of the Nystrom method. As part of the analysis, this work establishes a novel $1 + \epsilon$ relative-error trace norm guarantee for low-rank approximation using the rank-restricted Nystrom approximation. Empirical evaluations on the $8.1$ million instance MNIST8M dataset demonstrate the scalability and usefulness of kernel $k$-means clustering with Nystrom approximation. This work argues that spectral clustering using Nystrom approximation---a popular and computationally efficient, but theoretically unsound approach to non-linear clustering---should be replaced with the efficient and theoretically sound combination of kernel $k$-means clustering with Nystrom approximation. The superior performance of the latter approach is empirically verified.

Canonical Polyadic Decomposition (CPD) is a powerful technique for uncovering multilinear relationships in tensors. Current research in scalable CPD has focused on designing efficient decomposition algorithms for large sparse tensors that arise in machine learning and data mining applications. This work addresses the complementary need for efficient decomposition algorithms for large dense tensors that arise in signal processing applications. Such tensors are often highly skewed, with one mode (e.g., time) orders of magnitude larger than the others. We present an algorithm appropriate for MapReduce settings that uses both regularization and sketching to efficiently operate on such tensors. We have open-sourced an Apache Spark implementation of the algorithm and evaluate it on synthetic and real datasets to characterize the trade-offs in runtime and accuracy when using different types and combinations of regularization and sketching. We observe that a combination of random entry sketching plus Tikhonov regularization works best independent of the type or level of noise in the tensor. Similarly, we find that random entry sketching plus proximal regularization works best for ill-conditioned tensors. Further experiments demonstrate that the runtime scales sublinearly with the tensor size and highly sublinearly with the tensor rank. The use of regularization and sketching results in runtimes that are factors of 42-112× faster than those of the previous state-of-the-art MapReduce CPD implementation for large dense, skewed tensors, while having a negligible impact on the accuracy of the decompositions.

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 recent years word-embedding models have gained great popularity due to their remarkable performance on several tasks, including word analogy questions and caption generation.An unexpected "sideeffect" of such models is that their vectors often exhibit compositionality, i.e., adding two word-vectors results in a vector that is only a small angle away from the vector of a word representing the semantic composite of the original words, e.g., "man" + "royal" = "king".

Recent work by Nesterov and Stich (2016) showed that momentum can be used to accelerate the rate of convergence for block Gauss-Seidel in the setting where a fixed partitioning of the coordinates is chosen ahead of time. We show that this setting is too restrictive, constructing instances where breaking locality by running non-accelerated Gauss-Seidel with randomly sampled coordinates substantially outperforms accelerated Gauss-Seidel with any fixed partitioning. Motivated by this finding, we analyze the accelerated block Gauss-Seidel algorithm in the random coordinate sampling setting. Our analysis captures the benefit of acceleration with a new data-dependent parameter which is well behaved when the matrix sub-blocks are well-conditioned. Empirically, we show that accelerated Gauss-Seidel with random coordinate sampling provides speedups for large scale machine learning tasks when compared to non-accelerated Gauss-Seidel and the classical conjugate-gradient algorithm.

We address the statistical and optimization impacts of using classical sketch versus Hessian sketch to solve approximately the Matrix Ridge Regression (MRR) problem. Prior research has considered the effects of classical sketch on least squares regression (LSR), a strictly simpler problem. We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR—namely, it recovers nearly optimal solutions. In contrast, Hessian sketch does not have this guarantee; instead, the approximation error is governed by a subtle interplay between the “mass” in the responses and the optimal objective value. For both types of approximations, the regularization in the sketched MRR problem gives it significantly different statistical properties from the sketched LSR problem. In particular, there is a bias-variance trade-off in sketched MRR that is not present in sketched LSR. We provide upper and lower bounds on the biases and variances of sketched MRR; these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches. Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions. We establish theoretically and empirically that model averaging greatly decreases this gap. Thus, in the distributed setting, sketching combined with model averaging is a powerful technique that quickly obtains near-optimal solutions to the MRR problem while greatly mitigating the statistical risks incurred by sketching.

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.

In recent years, several feature encoding schemes for the bags-of-visual-words model have been proposed. While most of these schemes produce impressive results, they all share an important limitation: their high computational complexity makes it challenging to use them for large-scale problems. In this work, we propose an approximate locality-constrained encoding scheme that offers significantly better computational efficiency (~ 40×) than its exact counterpart, with comparable classification accuracy. Using the perturbation analysis of least-squares problems, we present a formal approximation error analysis of our approach, which helps distill the intuition behind the robustness of our method. We present a thorough set of empirical analyses on multiple standard data-sets, to assess the capability of our encoding scheme for its representational as well as discriminative accuracy.

Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral clustering is computing a few of the top eigenvectors of the (normalized) Laplacian matrix corresponding to the graph representing the data to be clustered. One way to speed up the computation of these eigenvectors is to use the “power method” from the numerical linear algebra literature. Although the power method has been empirically used to speed up spectral clustering, the theory behind this approach, to the best of our knowledge, remains unexplored. This paper provides the first such rigorous theoretical justification, arguing that a small number of power iterations suffices to obtain near-optimal partitionings using the approximate eigenvectors. Specifically, we prove that solving the k-means clustering problem on the approximate eigenvectors obtained via the power method gives an additive-error approximation to solving the k-means problem on the optimal eigenvectors.

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this challenge, we propose compact random feature maps (CRAFTMaps) to approximate polynomial kernels more concisely and accurately. We prove the error bounds of CRAFTMaps demonstrating their superior kernel reconstruction performance compared to the previous approximation schemes. We show how structured random matrices can be used to efficiently generate CRAFTMaps, and present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class classifiers. We present experiments on multiple standard data-sets with performance competitive with state-of-the-art results.

We reconsider randomized algorithms for the low-rank approximation of SPSD matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices. Our results highlight complementary aspects of sampling versus projection methods, and they point to differences between uniform and nonuniform sampling methods based on leverage scores. We complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods. These bounds are qualitatively superior to existing bounds— e.g., improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error.