Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling's performance is highly sensitive to the user-specified initial length scale hyperparameter. Moreover, Slice Sampling generally struggles with poorly scaled or strongly correlated distributions. This paper introduces Ensemble Slice Sampling, a new class of algorithms that bypasses such difficulties by adaptively tuning the length scale. Furthermore, Ensemble Slice Sampling's performance is immune to linear correlations by exploiting an ensemble of parallel walkers. These algorithms are trivial to construct, require no hand-tuning, and can easily be implemented in parallel computing environments. Empirical tests show that Ensemble Slice Sampling can improve efficiency by more than an order of magnitude compared to conventional MCMC methods on highly correlated target distributions such as the Autoregressive Process of Order 1 and the Correlated Funnel distribution.

Most work in algorithmic fairness to date has focused on discrete outcomes, such as deciding whether to grant someone a loan or not. In these classification settings, group fairness criteria such as independence, separation and sufficiency can be measured directly by comparing rates of outcomes between subpopulations. Many important problems however require the prediction of a real-valued outcome, such as a risk score or insurance premium. In such regression settings, measuring group fairness criteria is computationally challenging, as it requires estimating information-theoretic divergences between conditional probability density functions. This paper introduces fast approximations of the independence, separation and sufficiency group fairness criteria for regression models from their (conditional) mutual information definitions, and uses such approximations as regularisers to enforce fairness within a regularised risk minimisation framework. Experiments in real-world datasets indicate that in spite of its superior computational efficiency our algorithm still displays state-of-the-art accuracy/fairness tradeoffs.

Optimization is a central ingredient of machine learning. First-order optimization algorithms, for instance, are particularly popular for deep learning tasks due to their scalabilities to highdimensional problems, because they employ gradient but not higher-order information of objective functions for iteratively approximating minimizers. Among first-order methods, arguably the most used is gradient descent method (GD), or rather one of its variants, stochastic gradient descent method (SGD). Designed for objective functions that sum a large amount of terms, which for instance can originate from big data, SGD introduces a randomization mechanism of gradient subsampling to improve the scalability of GD (e.g., Zhang [2004], Moulines and Bach [2011], Roux et al. [2012]). Consequently, the iteration of SGD, unlike GD, is not deterministic even when it is started at a fixed initial condition.

We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynamics, we present a novel, scalable two-player RL algorithm, which is a sampling variant of the two-player policy gradient method. Our algorithm consistently outperforms existing baselines, in terms of generalization across different training and testing conditions, on several MuJoCo environments. Our experiments also show that, even for objective functions that entirely ignore potential environmental shifts, our sampling approach remains highly robust in comparison to standard RL algorithms.

We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators. Combining our estimator with REINFORCE, we obtain a policy gradient estimator and we reduce its variance using a built-in control variate which is obtained without additional model evaluations. The resulting estimator is closely related to other gradient estimators. Experiments with a toy problem, a categorical Variational Auto-Encoder and a structured prediction problem show that our estimator is the only estimator that is consistently among the best estimators in both high and low entropy settings.

Experimental measurements of physical systems often have a finite number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from experimental data implicitly assume that the measurements have higher intrinsic dimensionality than the underlying system---making coordinate identification a dimensionality reduction problem. Here, we study the opposite limit, in which hidden governing coordinates must be inferred from only a low-dimensional time series of measurements. Inspired by classical techniques for studying the strange attractors of chaotic systems, we introduce a general embedding technique for time series, consisting of an autoencoder trained with a novel latent-space loss function. We first apply our technique to a variety of synthetic and real-world datasets with known strange attractors, and we use established and novel measures of attractor fidelity to show that our method successfully reconstructs attractors better than existing techniques. We then use our technique to discover dynamical attractors in datasets ranging from patient electrocardiograms, to household electricity usage, to eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.

Uplift modeling has effectively been used in fields such as marketing and customer retention, to target those customers that are most likely to respond due to the campaign or treatment. Uplift models produce uplift scores which are then used to essentially create a ranking. We instead investigate to learn to rank directly by looking into the potential of learning-to-rank techniques in the context of uplift modeling. We propose a unified formalisation of different global uplift modeling measures in use today and explore how these can be integrated into the learning-to-rank framework. Additionally, we introduce a new metric for learning-to-rank that focusses on optimizing the area under the uplift curve called the promoted cumulative gain (PCG). We employ the learning-to-rank technique LambdaMART to optimize the ranking according to PCG and show improved results over standard learning-to-rank metrics and equal to improved results when compared with state-of-the-art uplift modeling. Finally, we show how learning-to-rank models can learn to optimize a certain targeting depth, however, these results do not generalize on the test set.

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) defined by a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize the discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing $q(x)$ to minimize this discrepancy produces a novel method for training unnormalized models which scales more gracefully than existing methods. The ability to both learn and compare models is a unique feature of the proposed method.

We propose a new optimization formulation for training federated learning models. The standard formulation has the form of an empirical risk minimization problem constructed to find a single global model trained from the private data stored across all participating devices. In contrast, our formulation seeks an explicit trade-off between this traditional global model and the local models, which can be learned by each device from its own private data without any communication. Further, we develop several efficient variants of SGD (with and without partial participation and with and without variance reduction) for solving the new formulation and prove communication complexity guarantees. Notably, our methods are similar but not identical to federated averaging / local SGD, thus shedding some light on the essence of the elusive method. In particular, our methods do not perform full averaging steps and instead merely take steps towards averaging. We argue for the benefits of this new paradigm for federated learning.

The continuous expansion of the urban traffic sensing infrastructure has led to a surge in the volume of widely available road related data. Consequently, increasing effort is being dedicated to the creation of intelligent transportation systems, where decisions on issues ranging from city-wide road maintenance planning to improving the commuting experience are informed by computational models of urban traffic instead of being left entirely to humans. The automation of traffic management has received substantial attention from the research community, however, most approaches target highways, produce predictions valid for a limited time window or require expensive retraining of available models in order to accurately forecast traffic at a new location. In this article, we propose a novel and accurate traffic flow prediction method based on symbolic regression enhanced with a lag operator. Our approach produces robust models suitable for the intricacies of urban roads, much more difficult to predict than highways. Additionally, there is no need to retrain the model for a period of up to 9 weeks. Furthermore, the proposed method generates models that are transferable to other segments of the road network, similar to, yet geographically distinct from the ones they were initially trained on. We demonstrate the achievement of these claims by conducting extensive experiments on data collected from the Darmstadt urban infrastructure.