Abstract: We develop a new scalable method for matrix completion via nuclear-norm regularization and alternating least squares. The algorithm has an EM flavor, which dramatically reduces the computational cost per iteration at the cost of more iterations. *joint work with Rahul Mazumder, Jason Lee and Reza Zadeh.

Abstract: Low-rank matrix estimation plays a key role in many scientific and engineering tasks, including collaborative filtering and image denoising. Low-rank procedures are often motivated by the statistical model where we observe a noisy matrix drawn from some distribution with expectation assumed to have a low-rank representation; the statistical goal is then to recover the signal from the noisy data. Given this setup, we develop a framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple parametric bootstrap. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is robust with respect to the specified noise model. In the simplest case, with an isotropic noise model, our procedure is equivalent to a classical singular value shrinkage estimator. For non-isotropic noise models, however, our method does not reduce to singular value shrinkage, and instead yields new estimators that perform well in experiments. Moreover, by iterating our stable autoencoding scheme, we can automatically generate low-rank estimates without specifying the target rank as a tuning parameter.

Abstract: The Behance social network allows professionals of diverse artistic disciplines to exhibit their work and connect amongst each other. We investigate the network properties of the UX/UI designer subgraph. Considering the subgraph is motivated by the idea that professionals in the same discipline are more likely to give a realistic assessment of a colleague's work. We therefore developed a metric to assess the in uence and importance of a specic member of the community based on structural properties of the subgraph and additional measures of prestige. For that purpose, we identied appreciations as a useful measure to include in a weighted PageRank algorithm, as it adds a notion of perceived quality of the work in the artist's portfolio to the ranking, which is not contained in the structural information of the graph. With this weighted PageRank, we identied locations that have a high density of in uential UX/UI designers.

Abstract: The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc-bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

Abstract: We use large (100k x 100k) sparse similarity matrices of time series (sensor data) for anomaly detection and failure prediction. These similarity matrices, computed using the universal information distance based on Kolmogorov Complexity, are used to perform non-parametric unsupervised clustering with non-linear boundaries without complex and slow coordinate transformations of the raw data. Changes over time in the similarity matrix allow us to observe anomalous behavior of the system and predict failure of parts. This approach is well suited for big data with little prior domain knowledge. Once we have learned the basic dependency patterns from the data, we can use this in addition to domain knowledge to build a causal model that relates outcomes to inputs through hidden variables. Given a set of observed outcomes and their associated sensor data, we can build a probabilistic model of the underlying causal events that produced both the outcomes and the data. The parameters of this probabilistic model (conditional joint probabilities) are inferred by maximizing the likelihood of the observed historical data. When such a model has been inferred, we can use it to predict future outcomes based on observations by first identifying the most likely underlying causal events that produced the observations and hence the most likely resulting outcomes. Both approaches differ from building a direct correlational model between the data and outcomes because they utilize complex representations of the state of the system -- in the first case through the similarity matrix and in the second case through domain specific modeling. As a final step, these predictions of future outcomes are fed into an over-arching stochastic optimization for optimal scheduling of maintenance activities over either short or long term time horizons. We’ll show real world examples from utilities, aerospace and defense and video surveillance. * It is a joint work with Alan McCord and Anand Murugan

Abstract: Targeting and Recommendation are major topics in ecommerce. The topic is treated as “Matrix Completion” in statistics. The main point is to compute the unknown (missing) values in the matrix data. This work is based on a different view of regularization, i.e., a localized regularization technique which leads to improvement in the estimation of the missing values.

Abstract: Though modern data often provides a massive amount of information, much of that might be redundant or useless (noise). Thus, it is significant to recognize the most informative features of data. This will help the analysis of the data by removing the consequences of high dimensionality, in addition of obtaining other advantages of lower dimensional data such as lower computational cost and a less complex model.

Abstract: The so-called influencer, a person with the ability to persuade people, have important role on the information diffusion in social media environments. Indeed, influencers might dictate word-of-mouth and peer recommendation, impacting tasks such as recommendation, advertising, brand evaluation, among others. Thus, a growing number of works aim to identify influencers by exploiting distinct information. Deciding about the best strategy for each domain, however, is a complex task due to the lack of consensus among these works. This paper presents a quantitative study of analysis among some of the main strategies for identifying influencers, aiming to help researchers on this decision. Besides determining semantic classes of strategies, based on the characteristics they exploit, we obtained through PCA an effective meta-learning process to combine linearly distinct strategies. As main implications, we highlight a better understanding about the selected strategies and a novel manner to alleviate the difficulty on deciding which strategy researchers would adopt.

Abstract: Kernel k-Means is a basis for many state of the art global clustering approaches. When the number of samples grows too big, however, it is extremely time consuming to compute the entire kernel matrix and it is impossible to store it in the memory of a single computer. The algorithm of Approximate Kernel k-Means has been proposed, which works using only a small part of the kernel matrix. The computation of the kernel matrix, even a part of it, remains a significant bottleneck of the process. Some types of kernel, however, can be computed using matrix multiplication. Modern CPU architectures and computational optimization methods allow for very fast matrix multiplication, thus those types of kernel matrices can be computed much faster than others.