Nonnegative Matrix Factorization (NMF) and Nonnegative Coupled Matrix Tensor Factorization (NCMTF) are Constrained Low-Rank Approximation (CLRA) models which have found use in many applications. In particular, NMF and its variants have been shown to produce high-quality soft clustering and topic modeling results with the property that each clustering assignment relates to a corresponding topic; thereby providing insight into the nature of each item in a given cluster. However, NMF and its variants are unable to process heterogeneous data represented as one or more coupled tenors. Similarly, there do not exist tensorized methods which fully preserve the aforementioned desirable clustering and topic modeling properties of NMF. This paper develops a higher order analog of Joint-NMF, Joint Nonnegative Coupled Matrix Tensor Factorization (Joint-NCMTF), capable of factorizing heterogeneous tensor datasets whilst fully preserving these NMF properties. To accomplish this, we develop higher-order analogs of the entire NMF process, including crucial pre and post-processing steps. By incorporating additional dimensions of information present in datasets posed as coupled higher-order tensors, our proposed Joint-NCMTF method yields higher quality clustering and topic modeling results than methods which incorporate less information. We empirically demonstrate the effectiveness of our proposed method on multiple synthetic and two real-world topic modeling tasks.

Rank selection, i.e. the choice of factorization rank, is the first step in constructing Nonnegative Matrix Factorization (NMF) models. It is a long-standing problem which is not unique to NMF, but arises in most models which attempt to decompose data into its underlying components. Since these models are often used in the unsupervised setting, the rank selection problem is further complicated by the lack of ground truth labels. In this paper, we review and empirically evaluate the most commonly used schemes for NMF rank selection.

This paper describes a new method for representing embedding tables of graph neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We consider the scenario where (a) the graph data that lack node features, thereby requiring the learning of embeddings during training; and (b) we wish to exploit GPU platforms, where smaller tables are needed to reduce host-to-GPU communication even for large-memory GPUs. The use of TT enables a compact parameterization of the embedding, rendering it small enough to fit entirely on modern GPUs even for massive graphs. When combined with judicious schemes for initialization and hierarchical graph partitioning, this approach can reduce the size of node embedding vectors by 1,659 times to 81,362 times on large publicly available benchmark datasets, achieving comparable or better accuracy and significant speedups on multi-GPU systems. In some cases, our model without explicit node features on input can even match the accuracy of models that use node features.

We propose CUP, a new method for compressing and accelerating deep neural networks. At its core, CUP achieves compression by clustering and pruning similar filters in each layer. For clustering, CUP uses hierarchical clustering which allows for an elegant parameterization of model capacity through a single hyper-parameter t. We observe that by increasing t, CUP can dynamically reduce model capacity through non-uniform layer-wise pruning leading to two advantages. First, CUP can effectively compress a model to within the desired compute budget through a simple line-search on t. Second, through a simple extension, CUP can obtain the pruned model in a single training pass leading to large savings in training time. On Imagenet, CUP leads to a 2.47× FLOPS reduction on Resnet-50 with less than 1% drop in top-5 accuracy. Notably, in the retrain-free setting, CUP-RF saves over 10 hours of training time on 3 GPUs, in comparison to state-of-the-art methods. The code for CUP is open sourced1.

This paper presents a new method, which we call SUSTain, that extends real-valued matrix and tensor factorizations to data where values are integers. Such data are common when the values correspond to event counts or ordinal measures. The conventional approach is to treat integer data as real, and then apply real-valued factorizations. However, doing so fails to preserve important characteristics of the original data, thereby making it hard to interpret the results. Instead, our approach extracts factor values from integer datasets as scores that are constrained to take values from a small integer set. These scores are easy to interpret: a score of zero indicates no feature contribution and higher scores indicate distinct levels of feature importance. At its core, SUSTain relies on: a) a problem partitioning into integer-constrained subproblems, so that they can be optimally solved in an efficient manner; and b) organizing the order of the subproblems' solution, to promote reuse of shared intermediate results. We propose two variants, SUSTain_M and SUSTain_T, to handle both matrix and tensor inputs, respectively. We evaluate SUSTain against several state-of-the-art baselines on both synthetic and real Electronic Health Record (EHR) datasets. Comparing to those baselines, SUSTain shows either significantly better fit or orders of magnitude speedups that achieve a comparable fit (up to 425× faster). We apply SUSTain to EHR datasets to extract patient phenotypes (i.e., clinically meaningful patient clusters). Furthermore, 87% of them were validated as clinically meaningful phenotypes related to heart failure by a cardiologist.

In exploratory tensor mining, a common problem is how to analyze a set of variables across a set of subjects whose observations do not align naturally. For example, when modeling medical features across a set of patients, the number and duration of treatments may vary widely in time, meaning there is no meaningful way to align their clinical records across time points for analysis purposes. To handle such data, the state-of-the-art tensor model is the so-called PARAFAC2, which yields interpretable and robust output and can naturally handle sparse data. However, its main limitation up to now has been the lack of efficient algorithms that can handle large-scale datasets.

We study the problem of Polyadic Prediction, where the input consists of an ordered tuple of objects, and the goal is to predict a measurement associated with them. Many tasks can be naturally framed as Polyadic Prediction problems. In drug discovery, for instance, it is important to estimate the treatment effect of a drug on various tissue-specific diseases, as it is expressed over the available genes. Thus, we essentially predict the expression value measurements for several (drug, gene, tissue) triads. To tackle Polyadic Prediction problems, we propose a general framework, called Polyadic Regression, predicting measurements associated with multiple objects. Our framework is inductive, in the sense of enabling predictions for new objects, unseen during training. Our model is expressive, exploring high-order, polyadic interactions in an efficient manner. An alternating Proximal Gradient Descent procedure is proposed to fit our model. We perform an extensive evaluation using real-world chemogenomics data, where we illustrate the superior performance of Polyadic Regression over the prior art. Our method achieves an increase of 0.06 and 0.1 in Spearman correlation between the predicted and the actual measurement vectors, for predicting missing polyadic data and predicting polyadic data for new drugs, respectively.

We propose a new tensor factorization method, called the Sparse Hierarchical-Tucker (Sparse H-Tucker), for sparse and high-order data tensors. Sparse H-Tucker is inspired by its namesake, the classical Hierarchical Tucker method, which aims to compute a tree-structured factorization of an input data set that may be readily interpreted by a domain expert. However, Sparse H-Tucker uses a nested sampling technique to overcome a key scalability problem in Hierarchical Tucker, which is the creation of an unwieldy intermediate dense core tensor, the result of our approach is a faster, more space-efficient, and more accurate method. We test our method on a real healthcare dataset, which is collected from 30K patients and results in an 18th order sparse data tensor. Unlike competing methods, Sparse H-Tucker can analyze the full data set on a single multi-threaded machine. It can also do so more accurately and in less time than the state-of-the-art: on a 12th order subset of the input data, Sparse H-Tucker is 18x more accurate and 7.5x faster than a previously state-of-the-art method. Moreover, we observe that Sparse H-Tucker scales nearly linearly in the number of non-zero tensor elements. The resulting model also provides an interpretable disease hierarchy, which is confirmed by a clinical expert.

Kernel summations are a ubiquitous key computational bottleneck in many data analysis methods.In this paper, we attempt to marry, for the first time, the best relevant techniques in parallel computing, where kernel summations are in low dimensions, with the best general-dimension algorithms from the machine learning literature.We provide the first distributed implementation of kernel summation framework that can utilize: 1) various types of deterministic and probabilistic approximations that may be suitable for low and high-dimensional problems with a large number of data points; 2) any multi-dimensional binary tree using both distributed memory and shared memory parallelism; 3) a dynamic load balancing scheme to adjust work imbalances during the computation.Our hybrid MPI/OpenMP codebase has wide applicability in providing a general framework to accelerate the computation of many popular machine learning methods.Our experiments show scalability results for kernel density estimation on a synthetic ten-dimensional dataset containing over one billion points and a subset of the Sloan Digital Sky Survey Data up to 6,144 cores. 23

We present a Java-based framework, SWAMI (Shared Wisdom through the Amalgamation of Many Interpretations) for building and studying collaborative filtering systems. SWAMI consists of three components: a prediction engine, an evaluation system, and a visualization component. The prediction engine provides a common interface for implementing different prediction algorithms. The evaluation system provides a standardized testing methodology and metrics for analyzing the accuracy and run-time performance of prediction algorithms. The visualization component suggests how graphical representations can inform the development and analysis of prediction algorithms. We demonstrate SWAMI on the Each Movie data set by comparing three prediction algorithms: a traditional Pearson correlation-based method, support vector machines, and a new accurate and scalable correlation-based method based on clustering techniques.