In a previous post I summarized the tasks and procedures available in SAS Viya Data Mining and Machine Learning. In this post, I'll dive into the unsupervised learning category which currently hosts several tasks: Kmeans, Kmodes, and Kprototypes Clustering, Outlier Detection, and a few variants of Principal Component Analysis. In unsupervised learning there are no known labels (outcomes), only attributes (inputs). Examples include clustering, association, and segmentation. Machine learning finds high density areas (in multidimensional space) that are more or less similar to each other, and identifies structures in the data that separate these areas.

To summarize, it's important to spend time extracting, selecting and constructing features based on your data and it's size. It will be valuable in improving the performance of your model. Some features could be selected from a given feature set based on correlation with other predictors or with the label. If you have a small set of features, a quick brute-force approach of attempting different combinations might give you the best set of predictors. If you have a huge feature set especially when compared to the total number of data points – exploring dimensionality reduction techniques or other methods to combine multiple features together might be of help. But ultimately, though some of the methods above would help pick features, it's up to you to evaluate their value in being good predictors.

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided which guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm converges quickly to a local minimum solution.

Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic embeddings, building on exponential family embeddings to capture how the meanings of words change over time. We use dynamic embeddings to analyze three large collections of historical texts: the U.S. Senate speeches from 1858 to 2009, the history of computer science ACM abstracts from 1951 to 2014, and machine learning papers on the Arxiv from 2007 to 2015. We find dynamic embeddings provide better fits than classical embeddings and capture interesting patterns about how language changes.

We propose a general approach to modeling semi-supervised learning (SSL) algorithms. Specifically, we present a declarative language for modeling both traditional supervised classification tasks and many SSL heuristics, including both well-known heuristics such as co-training and novel domain-specific heuristics. In addition to representing individual SSL heuristics, we show that multiple heuristics can be automatically combined using Bayesian optimization methods. We experiment with two classes of tasks, link-based text classification and relation extraction. We show modest improvements on well-studied link-based classification benchmarks, and state-of-the-art results on relation-extraction tasks for two realistic domains.

While significant progress has been made separately on analytics systems for scalable stochastic gradient descent (SGD) and private SGD, none of the major scalable analytics frameworks have incorporated differentially private SGD. There are two inter-related issues for this disconnect between research and practice: (1) low model accuracy due to added noise to guarantee privacy, and (2) high development and runtime overhead of the private algorithms. This paper takes a first step to remedy this disconnect and proposes a private SGD algorithm to address \emph{both} issues in an integrated manner. In contrast to the white-box approach adopted by previous work, we revisit and use the classical technique of {\em output perturbation} to devise a novel "bolt-on" approach to private SGD. While our approach trivially addresses (2), it makes (1) even more challenging. We address this challenge by providing a novel analysis of the $L_2$-sensitivity of SGD, which allows, under the same privacy guarantees, better convergence of SGD when only a constant number of passes can be made over the data. We integrate our algorithm, as well as other state-of-the-art differentially private SGD, into Bismarck, a popular scalable SGD-based analytics system on top of an RDBMS. Extensive experiments show that our algorithm can be easily integrated, incurs virtually no overhead, scales well, and most importantly, yields substantially better (up to 4X) test accuracy than the state-of-the-art algorithms on many real datasets.

Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of the end user and profitability. However, there is a growing concern that these automated decisions can lead, even in the absence of intent, to a lack of fairness, i.e., their outcomes can disproportionately hurt (or, benefit) particular groups of people sharing one or more sensitive attributes (e.g., race, sex). In this paper, we introduce a flexible mechanism to design fair classifiers by leveraging a novel intuitive measure of decision boundary (un)fairness. We instantiate this mechanism with two well-known classifiers, logistic regression and support vector machines, and show on real-world data that our mechanism allows for a fine-grained control on the degree of fairness, often at a small cost in terms of accuracy. A Python implementation of our mechanism is available at fate-computing.mpi-sws.org

There is an especially strong need in modern large-scale data analysis to prioritize samples for manual inspection. For example, the inspection could target important mislabeled samples or key vulnerabilities exploitable by an adversarial attack. In order to solve the "needle in the haystack" problem of which samples to inspect, we develop a new scalable version of Cook's distance, a classical statistical technique for identifying samples which unusually strongly impact the fit of a regression model (and its downstream predictions). In order to scale this technique up to very large and high-dimensional datasets, we introduce a new algorithm which we call "influence sketching." Influence sketching embeds random projections within the influence computation; in particular, the influence score is calculated using the randomly projected pseudo-dataset from the post-convergence Generalized Linear Model (GLM). We validate that influence sketching can reliably and successfully discover influential samples by applying the technique to a malware detection dataset of over 2 million executable files, each represented with almost 100,000 features. For example, we find that randomly deleting approximately 10% of training samples reduces predictive accuracy only slightly from 99.47% to 99.45%, whereas deleting the same number of samples with high influence sketch scores reduces predictive accuracy all the way down to 90.24%. Moreover, we find that influential samples are especially likely to be mislabeled. In the case study, we manually inspect the most influential samples, and find that influence sketching pointed us to new, previously unidentified pieces of malware.

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982}. The correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clustering algorithm, on the grounds of distance matrix. The scope of correction is explained in section 2.

We hear the term "machine learning" a lot these days, usually in the context of predictive analysis and artificial intelligence. Machine learning is, more or less, a way for computers to learn things without being specifically programmed. But how does that actually happen? The answer is, in one word, algorithms. Algorithms are sets of rules that a computer is able to follow.