A machine learning model may exhibit discrimination when used to make decisions involving people. One potential cause for such outcomes is that the model uses a statistical proxy for a protected demographic attribute. In this paper we formulate a definition of proxy use for the setting of linear regression and present algorithms for detecting proxies. Our definition follows recent work on proxies in classification models, and characterizes a model's constituent behavior that: 1) correlates closely with a protected random variable, and 2) is causally influential in the overall behavior of the model. We show that proxies in linear regression models can be efficiently identified by solving a second-order cone program, and further extend this result to account for situations where the use of a certain input variable is justified as a ``business necessity''. Finally, we present empirical results on two law enforcement datasets that exhibit varying degrees of racial disparity in prediction outcomes, demonstrating that proxies shed useful light on the causes of discriminatory behavior in models.

Decentralized machine learning is a promising emerging paradigm in view of global challenges of data ownership and privacy. We consider learning of linear classification and regression models, in the setting where the training data is decentralized over many user devices, and the learning algorithm must run on-device, on an arbitrary communication network, without a central coordinator. We propose COLA, a new decentralized training algorithm with strong theoretical guarantees and superior practical performance. Our framework overcomes many limitations of existing methods, and achieves communication efficiency, scalability, elasticity as well as resilience to changes in data and allows for unreliable and heterogeneous participating devices.

Subsampling is a common and often effective method to deal with the computational challengesof large datasets. However, for most statistical models, there is no well-motivated approach for drawing a nonuniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence function leads to asymptotically optimal sampling probabilities for a wide class of popular models. This is the only tight optimality result for subsampling we are aware of as other methods only provide probabilistic error bounds or optimal rates. We also show that these optimal weights can differ depending on whether the task is parameter estimationor prediction. Furthermore, for linear regression models, which have well-studied procedures for nonuniform subsampling, we empirically show our optimal influence function based method outperforms previous approaches even when using approximations to the optimal probabilities.

We propose a nonparametric derivative estimation method for random design without having to estimate the regression function. The method is based on a variance-reducing linear combination of symmetric difference quotients. First, we discuss the special case of uniform random design and establish the estimator’s asymptotic properties. Secondly, we generalize these results for any distribution of the dependent variable and compare the proposed estimator with popular estimators for derivative estimation such as local polynomial regression and smoothing splines.

We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the system is available. We consider the Nearest Neighbor Q-Learning (NNQL) algorithm to learn the optimal Q function using nearest neighbor regression method. As the main contribution, we provide tight finite sample analysis of the convergence rate. In particular, for MDPs with a $d$-dimensional state space and the discounted factor $\gamma \in (0,1)$, given an arbitrary sample path with ``covering time'' $L$, we establish that the algorithm is guaranteed to output an $\varepsilon$-accurate estimate of the optimal Q-function using $\Ot(L/(\varepsilon^3(1-\gamma)^7))$ samples. For instance, for a well-behaved MDP, the covering time of the sample path under the purely random policy scales as $\Ot(1/\varepsilon^d),$ so the sample complexity scales as $\Ot(1/\varepsilon^{d+3}).$ Indeed, we establish a lower bound that argues that the dependence of $ \Omegat(1/\varepsilon^{d+2})$ is necessary.

The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets. However, there has been limited success in deriving estimates for the full posterior distribution of regression coefficients in these models, due to a need to evaluate analytically intractable partition function integrals. Here, the Fourier transform is used to express these integrals as complex-valued oscillatory integrals over "regression frequencies". This results in an analytic expansion and stationary phase approximation for the partition functions of the Bayesian lasso and elastic net, where the non-differentiability of the double-exponential prior has so far eluded such an approach. Use of this approximation leads to highly accurate numerical estimates for the expectation values and marginal posterior distributions of the regression coefficients, and allows for Bayesian inference of much higher dimensional models than previously possible.

Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to the missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that is helpful. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods.

We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive a new margin-based regret bound in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an efficient algorithm with a $\sqrt{dT}$-type mistake bound against benchmark policies induced by $d$-dimensional regressors. Under realizability assumptions, our results also yield classical regret bounds.

Suppose an n x d design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number k << n of the responses, and then produce a weight vector whose sum of squares loss over *all* points is at most 1+epsilon times the minimum. When k is very small (e.g., k=d), jointly sampling diverse subsets of points is crucial. One such method called "volume sampling" has a unique and desirable property that the weight vector it produces is an unbiased estimate of the optimum. It is therefore natural to ask if this method offers the optimal unbiased estimate in terms of the number of responses k needed to achieve a 1+epsilon loss approximation. Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation -- indeed worse than some i.i.d. sampling techniques whose estimates are biased, such as leverage score sampling. We then develop a new rescaled variant of volume sampling that produces an unbiased estimate which avoids this bad behavior and has at least as good a tail bound as leverage score sampling: sample size k=O(d log d + d/epsilon) suffices to guarantee total loss at most 1+epsilon times the minimum with high probability. Thus, we improve on the best previously known sample size for an unbiased estimator, k=O(d^2/epsilon). Our rescaling procedure leads to a new efficient algorithm for volume sampling which is based on a "determinantal rejection sampling" technique with potentially broader applications to determinantal point processes. Other contributions include introducing the combinatorics needed for rescaled volume sampling and developing tail bounds for sums of dependent random matrices which arise in the process.

Multivariate time series usually contain a large number of missing values, which hinders the application of advanced analysis methods on multivariate time series data. Conventional approaches to addressing the challenge of missing values, including mean/zero imputation, case deletion, and matrix factorization-based imputation, are all incapable of modeling the temporal dependencies and the nature of complex distribution in multivariate time series. In this paper, we treat the problem of missing value imputation as data generation. Inspired by the success of Generative Adversarial Networks (GAN) in image generation, we propose to learn the overall distribution of a multivariate time series dataset with GAN, which is further used to generate the missing values for each sample. Different from the image data, the time series data are usually incomplete due to the nature of data recording process. A modified Gate Recurrent Unit is employed in GAN to model the temporal irregularity of the incomplete time series. Experiments on two multivariate time series datasets show that the proposed model outperformed the baselines in terms of accuracy of imputation. Experimental results also showed that a simple model on the imputed data can achieve state-of-the-art results on the prediction tasks, demonstrating the benefits of our model in downstream applications.