We describe two nonconventional algorithms for linear regression, called GAME and CLASH. The salient characteristics of these approaches is that they exploit the convex $\ell_1$-ball and non-convex $\ell_0$-sparsity constraints jointly in sparse recovery. To establish the theoretical approximation guarantees of GAME and CLASH, we cover an interesting range of topics from game theory, convex and combinatorial optimization. We illustrate that these approaches lead to improved theoretical guarantees and empirical performance beyond convex and non-convex solvers alone.

Nowadays web users actively generate content on different social media platforms. The large number of users requiring personalized services creates a unique opportunity for researchers to explore user modelling. Substantial research has been done by utilizing user generated content to model users by applying different classification or regression techniques. These techniques are powerful types of machine learning approaches, however they only partially model social media users. In this work, we introduce a new statistical relational learning (SRL) framework suitable for this purpose, which we call PSL Q . PSL Q is the first SRL framework that supports reasoning with soft quantifiers, such as “most” and “a few”. Indeed, in models for social media it is common to assume that friends are influenced by each other’s behavior, beliefs, and preferences. Thus, having a trait only becomes probable once most or some of one’s friends have that trait. Expressing this dependency requires a soft quantifier, which can be modeled with PSL^Q. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results.

Markov chain Monte Carlo (MCMC) is a popular tool for Bayesian inference.However, MCMC cannot be practically applied to large data sets because of theprohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) MCMC algorithm with auxiliary variables that only queries the likelihoods of a subset of the data at each iteration yet simulates from the exact posterior distribution. FlyMC is compatible with modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors. In experiments, we find that FlyMC generates samples from the posterior more than an order of magnitude faster than regular MCMC, allowing MCMC methods to tackle larger datasets than were previously considered feasible.

Domain adaptation aims at learning robust classifiers across domains using labeled data from a source domain. Representation learning methods, which project the original features to a new feature space, have been proved to be quite effective for this task. However, these unsupervised methods neglect the domain information of the input and are not specialized for the classification task. In this work, we address two key factors to guide the representation learning process for domain adaptation of sentiment classification — one is domain supervision, enforcing the learned representation to better predict the domain of an input, and the other is sentiment supervision which utilizes the source domain sentiment labels to learn sentiment-favorable representations. Experimental results show that these two factors significantly improve the proposed models as expected.

Differential privacy preserving regression models guarantee protection against attempts to infer whether a subject was included in the training set used to derive a model. It is not designed to protect attribute privacy of a target individual when model inversion attacks are launched. In model inversion attacks, an adversary uses the released model to make predictions of sensitive attributes (used as input to the model) of a target individual when some background information about the target individual is available. Previous research showed that existing differential privacy mechanisms cannot effectively prevent model inversion attacks while retaining model efficacy. In this paper, we develop a novel approach which leverages the functional mechanism to perturb coefficients of the polynomial representation of the objective function but effectively balances the privacy budget for sensitive and non-sensitive attributes in learning the differential privacy preserving regression model. Theoretical analysis and empirical evaluations demonstrate our approach can effectively prevent model inversion attacks and retain model utility.

Recently, several Web-scale knowledge harvesting systems have been built, each of which is competent at extracting information from certain types of data (e.g., unstructured text, structured tables on the web, etc.). In order to determine the response to a new query posed to such systems (e.g., is sugar a healthy food?), it is useful to integrate opinions from multiple systems. If a response is desired within a specific time budget (e.g., in less than 2 seconds), then maybe only a subset of these resources can be queried. In this paper, we address the problem of knowledge integration for on-demand time-budgeted query answering. We propose a new method, AskWorld, which learns a policy that chooses which queries to send to which resources, by accommodating varying budget constraints that are available only at query (test) time. Through extensive experiments on real world datasets, we demonstrate AskWorld’s capability in selecting most informative resources to query within test-time constraints, resulting in improved performance compared to competitive baselines.

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) approach to this problem using operator-valued kernels. Our formulation overcomes the two main limitations of the original KDE approach, namely the decoupling between outputs in the image space and the inability to use a joint feature space. We then propose a covariance-based operator-valued kernel that allows us to take into account the structure of the kernel feature space. This kernel operates on the output space and only encodes the interactions between the outputs without any reference to the input space. To address this issue, we introduce a variant of our KDE method based on the conditional covariance operator that in addition to the correlation between the outputs takes into account the effects of the input variables. Finally, we evaluate the performance of our KDE approach on three structured output problems, and compare it to the state-of-the-art kernelbased structured output regression methods.

In standard nonparametric regression analysis, most of the methods developed so far are based on the least square loss function for estimating conditional expectations. In many applications, however, it is required to study conditional distributions beyond means. A nice tool for this purpose was offered by [20] in the form of quantile regression, which allows both the location and the spread of the response variable to be studied by using asymmetric least absolute deviation loss function (ALAD). We refer the reader to [19, 37, 9, 33] and references therein, for details description and different estimation methods for quantile regression.

Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because they fit well with modern parallel computing architectures. We propose a simple measure of {\em concordance} between a design matrix and a subset of its rows that estimates how well a subset captures the variance-covariance structure of a larger data set. We illustrate the use of this measure in a heuristic method for selecting row partition sizes that balance statistical and computational efficiency goals in real-world problems.

In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem of choosing $k$ out of $p$ features in linear regression given $n$ observations. We develop a discrete extension of modern first order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with $n$ in the 1000s and $p$ in the 100s in minutes to provable optimality, and finds near optimal solutions for $n$ in the 100s and $p$ in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than {\texttt {Lasso}} and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.