Embedded feature selection is effective when both prediction and interpretation are needed. The Lasso and its extensions are standard methods for selecting a subset of features while optimizing a prediction function. In this paper, we are interested in embedded feature selection for multidimensional data, wherein (1) there is no need to reshape the multidimensional data into vectors and (2) structural information from multiple dimensions are taken into account. Our main contribution is a new method called Regularized multilinear regression and selection (Remurs) for automatically selecting a subset of features while optimizing prediction for multidimensional data. Both nuclear norm and the ℓ 1 -norm are carefully incorporated to derive a multi-block optimization algorithm with proved convergence. In particular, Remurs is motivated by fMRI analysis where the data are multidimensional and it is important to find the connections of raw brain voxels with functional activities. Experiments on synthetic and real data show the advantages of Remurs compared to Lasso, Elastic Net, and their multilinear extensions.

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most informative observations; we characterize its performance and fundamental lower bounds. We extend the algorithm and its guarantees to sparse linear regression in high-dimensional settings. Simulations suggest the algorithm is remarkably robust: it provides significant benefits over passive random sampling in real-world datasets that exhibit high nonlinearity and high dimensionality — significantly reducing both the mean and variance of the squared error.

We present a non-negative inductive latent factor model for binary- and count-valued matrices containing dyadic data, with side information along the rows and/or the columns of the matrix. The side information is incorporated by conditioning the row and column latent factors on the available side information via a regression model. Our model can not only perform matrix factorization and completion with side-information, but also infers interpretable latent topics that explain/summarize the data. An appealing aspect of our model is in the full local conjugacy of all parts of the model, including the main latent factor model, as well as for the regression model that leverages the side information. This enables us to design scalable and simple to implement Gibbs sampling and Expectation Maximization algorithms for doing inference in the model. Inference cost in our model scales in the number of nonzeros in the data matrix, which makes it particularly attractive for massive, sparse matrices. We demonstrate the effectiveness of our model on several real-world data sets, comparing it with state-of-the-art baselines.

Clustering is a fundamental research topic in data mining. A balanced clustering result is often required in a variety of applications. Many existing clustering algorithms have good clustering performances, yet fail in producing balanced clusters. In this paper, we propose a novel and simple method for clustering, referred to as the Balanced Clustering with Least Square regression (BCLS), to minimize the least square linear regression, with a balance constraint to regularize the clustering model. In BCLS, the linear regression is applied to estimate the class-specific hyperplanes that partition each class of data from others, thus guiding the clustering of the data points into different clusters. A balance constraint is utilized to regularize the clustering, by minimizing which can help produce balanced clusters. In addition, we apply the method of augmented Lagrange multipliers (ALM) to help optimize the objective model. The experiments on seven real-world benchmarks demonstrate that our approach not only produces good clustering performance but also guarantees a balanced clustering result.

Inferring causal relations from observational data is widely used for knowledge discovery in healthcare and economics. To investigate whether a treatment can affect an outcome of interest, we focus on answering counterfactual questions of this type: what would a patient’s blood pressure be had he/she received a different treatment? Nearest neighbor matching (NNM) sets the counterfactual outcome of any treatment (control) sample to be equal to the factual outcome of its nearest neighbor in the control (treatment) group. Although being simple, flexible and interpretable, most NNM approaches could be easily misled by variables that do not affect the outcome. In this paper, we address this challenge by learning subspaces that are predictive of the outcome variable for both the treatment group and control group. Applying NNM in the learned subspaces leads to more accurate estimation of the counterfactual outcomes and therefore treatment effects. We introduce an informative subspace learning algorithm by maximizing the nonlinear dependence between the candidate subspace and the outcome variable measured by the Hilbert-Schmidt Independence Criterion (HSIC). We propose a scalable estimator of HSIC, called HSIC-RFF that reduces the quadratic computational and storage complexities (with respect to the sample size) of the naive HSIC implementation to linear through constructing random Fourier features. We also prove an upper bound on the approximation error of the HSIC-RFF estimator. Experimental results on simulated datasets and real-world datasets demonstrate our proposed approach outperforms existing NNM approaches and other commonly used regression-based methods for counterfactual inference.

The cold-start problem involves recommendation of content to new users of a system, for whom there is no historical preference information available. This proves a challenge for collaborative filtering algorithms that inherently rely on such information. Recent work has shown that social metadata, such as users' friend groups and page likes, can strongly mitigate the problem. However, such approaches either lack an interpretation as optimising some principled objective, involve iterative non-convex optimisation with limited scalability, or require tuning several hyperparameters. In this paper, we first show how three popular cold-start models are special cases of a linear content-based model, with implicit constraints on the weights. Leveraging this insight, we propose Loco, a new model for cold-start recommendation based on three ingredients: (a) linear regression to learn an optimal weighting of social signals for preferences, (b) a low-rank parametrisation of the weights to overcome the high dimensionality common in social data, and (c) scalable learning of such low-rank weights using randomised SVD. Experiments on four real-world datasets show that Loco yields significant improvements over state-of-the-art cold-start recommenders that exploit high-dimensional social network metadata.

We examine the surveying problem, where we attempt to predict how a target user is likely to respond to questions by iteratively querying that user, collaboratively based on the responses of a sample set of users. We focus on an active learning approach, where the next question we select to ask the user depends on their responses to the previous questions. We propose a method for solving the problem based on a Bayesian dimensionality reduction technique. We empirically evaluate our method, contrasting it to benchmark approaches based on augmented linear regression, and show that it achieves much better predictive performance, and is much more robust when there is missing data.

Multi-Touch Attribution studies the effects of various types of online advertisements on purchase conversions. It is a very important problem in computational advertising, as it allows marketers to assign credits for conversions to different advertising channels and optimize advertising campaigns. In this paper, we propose an additional multi-touch attribution model (AMTA) based on two obvious assumptions: (1) the effect of an ad exposure is fading with time and (2) the effects of ad exposures on the browsing path of a user are additive.AMTA borrows the techniques from survival analysis and uses the hazard rate to measure the influence of an ad exposure. In addition, we both take the conversion time and the intrinsic conversion rate of users into consideration.Experimental results on a large real-world advertising dataset illustrate that the our proposed method is superior to state-of-the-art techniques in conversion rate prediction and the credit allocation based on AMTA is reasonable.

Inferring the latent emotive content of a narrative requires consideration of para-linguistic cues (e.g. pitch), linguistic content (e.g. vocabulary) and the physiological state of the narrator (e.g. heart-rate). In this study we utilized a combination of auditory, text, and physiological signals to predict the mood (happy or sad) of 31 narrations from subjects engaged in personal story-telling. We extracted 386 audio and 222 physiological features (using the Samsung Simband) from the data. A subset of 4 audio, 1 text, and 5 physiologic features were identified using Sequential Forward Selection (SFS) for inclusion in a Neural Network (NN). These features included subject movement, cardiovascular activity, energy in speech, probability of voicing, and linguistic sentiment (i.e. negative or positive). We explored the effects of introducing our selected features at various layers of the NN and found that the location of these features in the network topology had a significant impact on model performance. To ensure the real-time utility of the model, classification was performed over 5 second intervals. We evaluated our model’s performance using leave-one-subject-out crossvalidation and compared the performance to 20 baseline models and a NN with all features included in the input layer.

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose expectile matrix factorization by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.