With widespread use of machine learning methods in numerous domains involving humans, several studies have raised questions about the potential for unfairness towards certain individuals or groups. A number of recent works have proposed methods to measure and eliminate unfairness from machine learning models. However, most of this work has focused on only one dimension of fair decision making: distributive fairness, i.e., the fairness of the decision outcomes. In this work, we leverage the rich literature on organizational justice and focus on another dimension of fair decision making: procedural fairness, i.e., the fairness of the decision making process. We propose measures for procedural fairness that consider the input features used in the decision process, and evaluate the moral judgments of humans regarding the use of these features. We operationalize these measures on two real world datasets using human surveys on the Amazon Mechanical Turk (AMT) platform, demonstrating that our measures capture important properties of procedurally fair decision making. We provide fast submodular mechanisms to optimize the tradeoff between procedural fairness and prediction accuracy. On our datasets, we observe empirically that procedural fairness may be achieved with little cost to outcome fairness, but that some loss of accuracy is unavoidable.

This paper proposes a computational approach for analysis of strokes in line drawings by artists. We aim at developing an AI methodology that facilitates attribution of drawings of unknown authors in a way that is not easy to be deceived by forged art. The methodology used is based on quantifying the characteristics of individual strokes in drawings. We propose a novel algorithm for segmenting individual strokes. We propose an approach that combines different hand-crafted and learned features for the task of quantifying stroke characteristics. We experimented with a dataset of 300 digitized drawings with over 80 thousands strokes. The collection mainly consisted of drawings of Pablo Picasso, Henry Matisse, and Egon Schiele, besides a small number of representative works of other artists. The experiments shows that the proposed methodology can classify individual strokes with accuracy 70%-90%, and aggregate over drawings with accuracy above 80%, while being robust to be deceived by fakes.

The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific example of the sparse GLM. Among them, we focus on the robust and sparse linear regression based on the $\gamma$-divergence. The estimator of the $\gamma$-divergence has strong robustness under heavy contamination. In this paper, we extend the robust and sparse linear regression based on the $\gamma$-divergence to the robust and sparse GLM based on the $\gamma$-divergence with a stochastic optimization approach in order to obtain the estimate. We adopt the randomized stochastic projected gradient descent as a stochastic optimization approach and extend the established convergence property to the classical first-order necessary condition. By virtue of the stochastic optimization approach, we can efficiently estimate parameters for very large problems. Particularly, we show the linear regression, logistic regression and Poisson regression with $L_1$ regularization in detail as specific examples of robust and sparse GLM. In numerical experiments and real data analysis, the proposed method outperformed comparative methods.

Many information retrieval tasks rely on high dimensional searches, including K-nearest neighbors (KNN), approximate nearest neighbors (ANN), and exact r-neighbor lookup in Hamming space. At scale, these searches are enabled by indexes on binary hashes, such as locality-sensitive hashing (LSH) and multi-indexing [1]. Recent research has flourished on these topics due to enormous growth in data volume and industry applications [2]. We present a powerful new approach to a fundamental challenge in these tasks: learning a good binary hash function. We demonstrate the effectiveness of our method by applying it to the task of automated scene matching (ASM) with a multi-index system. We call our model convolutional hashing for automated scene matching (CHASM). To the best of our knowledge, it is the first neural network to outperform state-of-the-art hash functions like Haar wavelets and color layout descriptors at ASM across the board.

In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transformation associated with the assigned label. Generated pseudo observation-label pairs are subsequently used to train a neural network with Auto-clustering Output Layer (ACOL) that introduces multiple softmax nodes for each pseudo parent-class. Due to the unsupervised objective based on Graph-based Activity Regularization (GAR) terms, softmax duplicates of each parent-class are specialized as the hidden information captured through the help of domain specific transformations is propagated during training. Ultimately we obtain a k-means friendly latent representation. Furthermore, we demonstrate how the chosen transformation type impacts performance and helps propagate the latent information that is useful in revealing unknown clusters. Our results show state-of-the-art performance for unsupervised clustering tasks on MNIST, SVHN and USPS datasets, with the highest accuracies reported to date in the literature.

We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an $n$-$\ell_1$ cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from compressive measurements. Our method processes a data vector of the stream per time instance from a small number of measurements in contrast to conventional batch RPCA, which needs to access full data. The $n$-$\ell_1$ cluster-weighted minimization leverages the sparse components along with their correlations with multiple previously-recovered sparse vectors. Moreover, the proposed minimization can exploit the structures of sparse components via clustering and re-weighting iteratively. The method outperforms the existing methods for both numerical data and actual video data.

Subjective classification of galaxies can mislead us in the quest of the origin regarding formation and evolution of galaxies. Multivariate analyses are the best tools used for such kind of purpose to better understand the differences between various objects, in an objective manner. In the present study an objective classification of 362~923 galaxies of the Value Added Galaxy Catalogue (VAGC) is carried out with the help of three methods of multivariate analysis. First, independent component analysis (ICA) is used to determine a set of derived independent variables that are linear combinations of various observed parameters (viz. ionized lines, Lick indices, photometric and morphological parameters, star formation rates etc.) of the galaxies. Subsequently, K-means cluster analysis (CA) is applied on the independent components to find the optimum number of homogeneous groups. Finally, a stepwise multiple regression is carried out on each group to predict and study the star formation rate as a function of other independent observables. The properties of the ten groups thus uncovered, are used to explain their formation and evolution mechanisms. It is suggested that three groups are young and metal poor, belonging to the blue sequence, three others are old and metal rich (red sequence). The remaining four groups of intermediate ages cannot be classified in this bimodal sequence: two belong to a pronounced mixture of early and late type galaxies whereas the other two mostly contain old early type galaxies. The above result is indicative of a continuous evolutionary scenario of galaxies instead of two discrete modes, blue and red, so far suggested by previous authors. Some of our groups occupy the transition region with different quenching mechanisms. This establishes the elegance of a multivariate analysis giving rise to a sophisticated refinement over subjective inference.

The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a Bayes-frequentist consolidated data analysis workflow that is more effective than either of the two separately. In this paper, we propose the idea of "Bayes via goodness of fit" as a framework for exploring these fundamental questions, in a way that is general enough to embrace almost all of the familiar probability models. Several illustrative examples show the benefit of this new point of view as a practical data analysis tool. Relationship with other Bayesian cultures is also discussed.

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several approaches have been proposed in the past to address this serious limitation. In this work we investigate a decomposition strategy that learns on small, spatially defined data chunks. Our contributions are two fold: On the theoretical side we establish an oracle inequality for the overall learning method using the hinge loss, and show that the resulting rates match those known for SVMs solving the complete optimization problem with Gaussian kernels. On the practical side we compare our approach to learning SVMs on small, randomly chosen chunks. Here it turns out that for comparable training times our approach is significantly faster during testing and also reduces the test error in most cases significantly. Furthermore, we show that our approach easily scales up to 10 million training samples: including hyper-parameter selection using cross validation, the entire training only takes a few hours on a single machine. Finally, we report an experiment on 32 million training samples. All experiments used liquidSVM (Steinwart and Thomann, 2017).