Fairness has emerged as a key issue in machine learning as it is increasingly used in areas like hiring [Dastin, 2018], healthcare[Gupta and Mohammad, 2017], and criminal justice [Equivant, 2019]. In particular, models' predictions should not lead to decisions that discriminate on the basis of a legally protected attribute, such as race or gender. Among the proposals to address this issue, a growing body of work focuses on learning et al., 2017, del Barrio et al., 2018, Feldmanfair representations of data for downstream modeling [Calmon 2015, Johndrow and Lum, 2019, Kamiran and Calders, 2012]. Most of these approaches are modelet al., agnostic, which provides flexibility when working with the learned representations, but comes at the cost of potentially suboptimal results in terms of both fairness and accuracy. In this work, we present a new approach for fair representation learning that takes into account the target hypothesis class of models that will be learned from the representation. Specifically, we show how to leverage information about the reproducing kernel Hilbert space (RKHS) to learn a fair representation for kernel-based models with provable fairness and accuracy guarantees. Our approach builds on the classic Sufficient Dimension Reduction (SDR) framework [Li, 1991, Cook 1991, Cook, 1998, Fukumizu et al., 2004, 2009, Wu et al., 2009, Cook and Forzani, 2009]and Weisberg, which is used to compute a low-dimensional projection of the feature vector X that captures all information related to the response Y. Our key insight is that we can instead perform SDR with respect to the protected attributes S, and then take the orthogonal complement of the resulting projection to obtain a fair subspace of the RKHS that captures information in X unrelated to S. We show that functions in the fair subspace 2.2), and we leverage this fact to prove that our approachwill be independent of S under mild conditions (§

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to transform a source dataset to match a target dataset using the Wasserstein distance as a divergence measure. We introduce a hierarchical formulation of OT which leverages clustered structure in data to improve alignment in noisy, ambiguous, or multimodal settings. To solve this numerically, we propose a distributed ADMM algorithm that also exploits the Sinkhorn distance, thus it has an efficient computational complexity that scales quadratically with the size of the largest cluster. When the transformation between two datasets is unitary, we provide performance guarantees that describe when and how well aligned cluster correspondences can be recovered with our formulation, as well as provide worst-case dataset geometry for such a strategy. We apply this method to synthetic datasets that model data as mixtures of low-rank Gaussians and study the impact that different geometric properties of the data have on alignment. Next, we applied our approach to a neural decoding application where the goal is to predict movement directions and instantaneous velocities from populations of neurons in the macaque primary motor cortex. Our results demonstrate that when clustered structure exists in datasets, and is consistent across trials or time points, a hierarchical alignment strategy that leverages such structure can provide significant improvements in cross-domain alignment.

Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network parameters, leading to substantially better optimization results.

Due to the surprisingly good representation power of complex distributions, neural network (NN) classifiers are widely used in many tasks which include natural language processing, computer vision and cyber security. In recent works, people noticed the existence of adversarial examples. These adversarial examples break the NN classifiers' underlying assumption that the environment is attack free and can easily mislead fully trained NN classifier without noticeable changes. Among defensive methods, adversarial training is a popular choice. However, original adversarial training with single-step adversarial examples (Single-Adv) can not defend against iterative adversarial examples. Although adversarial training with iterative adversarial examples (Iter-Adv) can defend against iterative adversarial examples, it consumes too much computational power and hence is not scalable. In this paper, we analyze Iter-Adv techniques and identify two of their empirical properties. Based on these properties, we propose modifications which enhance Single-Adv to perform competitively as Iter-Adv. Through preliminary evaluation, we show that the proposed method enhances the test accuracy of state-of-the-art (SOTA) Single-Adv defensive method against iterative adversarial examples by up to 16.93% while reducing its training cost by 28.75%.

To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the objects are typically embedded in a Euclidean space while satisfying as many triplet comparisons as possible. In this paper, we introduce empirical uncertainty estimates for standard embedding algorithms when few noisy triplets are available, using a bootstrap and a Bayesian approach. In particular, simulations show that these estimates are well calibrated and can serve to select embedding parameters or to quantify uncertainty in scientific applications.

Integer-valued and count data are ubiquitous in many fields, including epidemiology (Osthus et al., 2018; Kowal, 2019), ecology (Dorazio et al., 2005), and insurance (Bening and Korolev, 2012), among others (Cameron and Trivedi, 2013). Count data also serve as an indicator of demand, such as the demand for medical services (Deb and Trivedi, 1997), emergency medical services (Matteson et al., 2011), and call center access (Shen and Huang, 2008). In these applications and many others, integer-valued data are frequently observed jointly with predictors, over time intervals, or across spatial locations. Integer-valued data also exhibit a variety of distributional features, including zero-inflation, skewness, over-or underdispersion, and in some cases may be bounded or censored. Flexible and interpretable models for integervalued processes are therefore highly useful in practice. The most widely-used models for count data build upon the Poisson distribution. However, the limitations of the Poisson distribution are well-known: the distribution is not sufficiently flexible in practice and cannot account for zero-inflation or over-and underdispersion. A common strategy is to generalize the Poisson model by introducing additional parameters.

Hyperparameter tuning is an omnipresent problem in machine learning as it is an integral aspect of obtaining the state-of-the-art performance for any model. Most often, hyperparameters are optimized just by training a model on a grid of possible hyperparameter values and taking the one that performs best on a validation sample (grid search). More recently, methods have been introduced that build a so-called surrogate model that predicts the validation loss for a specific hyperparameter setting, model and dataset and then sequentially select the next hyperparameter to test, based on a heuristic function of the expected value and the uncertainty of the surrogate model called acquisition function (sequential model-based Bayesian optimization, SMBO). In this paper we model the hyperparameter optimization problem as a sequential decision problem, which hyperparameter to test next, and address it with reinforcement learning. This way our model does not have to rely on a heuristic acquisition function like SMBO, but can learn which hyperparameters to test next based on the subsequent reduction in validation loss they will eventually lead to, either because they yield good models themselves or because they allow the hyperparameter selection policy to build a better surrogate model that is able to choose better hyperparameters later on. Experiments on a large battery of 50 data sets demonstrate that our method outperforms the state-of-the-art approaches for hyperparameter learning.

In this paper, we performed two types of software experiments to study the numerosity classification (subitizing) in humans and machines. Experiments focus on a particular kind of task is referred to as Semantic MNIST or simply SMNIST where the numerosity of objects placed in an image must be determined. The experiments called SMNIST for Humans are intended to measure the capacity of the Object File System in humans. In this type of experiment the measurement result is in well agreement with the value known from the cognitive psychology literature. The experiments called SMNIST for Machines serve similar purposes but they investigate existing, well known (but originally developed for other purpose) and under development deep learning computer programs. These measurement results can be interpreted similar to the results from SMNIST for Humans. The main thesis of this paper can be formulated as follows: in machines the image classification artificial neural networks can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of OFS in humans. Finally, we outline a conceptual framework to investigate the notion of number in humans and machines.

Policy gradient based reinforcement learning algorithms coupled with neural networks have shown success in learning complex policies in the model free continuous action space control setting. However, explicitly parameterized policies are limited by the scope of the chosen parametric probability distribution. We show that alternatively to the likelihood based policy gradient, a related objective can be optimized through advantage weighted quantile regression. Our approach models the policy implicitly in the network, which gives the agent the freedom to approximate any distribution in each action dimension, not limiting its capabilities to the commonly used unimodal Gaussian parameterization. This broader spectrum of policies makes our algorithm suitable for problems where Gaussian policies cannot fit the optimal policy. Moreover, our results on the MuJoCo physics simulator benchmarks are comparable or superior to state-of-the-art on-policy methods.

Automatic detection of colonic polyps is still an unsolved problem due to the large variation of polyps in terms of shape, texture, size, and color, and the existence of various polyp-like mimics during colonoscopy. In this study, we apply a recent region based convolutional neural network (CNN) approach for the automatic detection of polyps in images and videos obtained from colonoscopy examinations. We use a deep-CNN model (Inception Resnet) as a transfer learning scheme in the detection system. To overcome the polyp detection obstacles and the small number of polyp images, we examine image augmentation strategies for training deep networks. We further propose two efficient post-learning methods such as, automatic false positive learning and off-line learning, both of which can be incorporated with the region based detection system for reliable polyp detection. Using the large size of colonoscopy databases, experimental results demonstrate that the suggested detection systems show better performance compared to other systems in the literature. Furthermore, we show improved detection performance using the proposed post-learning schemes for colonoscopy videos.