Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the stochastic gradient descent algorithm and apply a pre-defined sensitivity to the gradients for privatizing weights. However, their slow convergence typically yields a high cumulative privacy loss. Here, we take a different route by employing the method of auxiliary coordinates, which allows us to independently update the weights per layer by optimizing a per-layer objective function. This objective function can be well approximated by a low-order Taylor's expansion, in which sensitivity analysis becomes tractable. We perturb the coefficients of the expansion for privacy, which we optimize using more advanced optimization routines than SGD for faster convergence. We empirically show that our algorithm provides a decent trained model quality under a modest privacy budget.

We generalize the concept of maximum-margin classifiers (MMCs) to arbitrary norms and non-linear functions. Support Vector Machines (SVMs) are a special case of MMC. We find that MMCs can be formulated as Integral Probability Metrics (IPMs) or classifiers with some form of gradient norm penalty. This implies a direct link to a class of Generative adversarial networks (GANs) which penalize a gradient norm. We show that the Discriminator in Wasserstein, Standard, Least-Squares, and Hinge GAN with Gradient Penalty is an MMC. We explain why maximizing a margin may be helpful in GANs. We hypothesize and confirm experimentally that $L^\infty$-norm penalties with Hinge loss produce better GANs than $L^2$-norm penalties (based on common evaluation metrics). We derive the margins of Relativistic paired (Rp) and average (Ra) GANs.

We propose a novel strategy for extracting features in supervised learning that can be used to construct a classifier which is more robust to small perturbations in the input space. Our method builds upon the idea of the information bottleneck by introducing an additional penalty term that encourages the Fisher information of the extracted features to be small, when parametrized by the inputs. By tuning the regularization parameter, we can explicitly trade off the opposing desiderata of robustness and accuracy when constructing a classifier. We derive the optimal solution to the robust information bottleneck when the inputs and outputs are jointly Gaussian, proving that the optimally robust features are also jointly Gaussian in that setting. Furthermore, we propose a method for optimizing a variational bound on the robust information bottleneck objective in general settings using stochastic gradient descent, which may be implemented efficiently in neural networks. Our experimental results for synthetic and real data sets show that the proposed feature extraction method indeed produces classifiers with increased robustness to perturbations.

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our analysis and experiments reveal that certain higher-order moments of the stochastic gradient are able to achieve better performance compared to the vanilla Adam algorithm. We also provide some analysis of HAdam related to odd and even moments to explain some intriguing and seemingly non-intuitive empirical results.

In this paper we analyze, evaluate, and improve the performance of training Random Forest (RF) models on modern CPU architectures. An exact, state-of-the-art binary decision tree building algorithm is used as the basis of this study. Firstly, we investigate the trade-offs between using different tree building algorithms, namely breadth-first-search (BFS) and depth-search-first (DFS). We design a novel, dynamic, hybrid BFS-DFS algorithm and demonstrate that it performs better than both BFS and DFS, and is more robust in the presence of workloads with different characteristics. Secondly, we identify CPU performance bottlenecks when generating trees using this approach, and propose optimizations to alleviate them. The proposed hybrid tree building algorithm for RF is implemented in the Snap Machine Learning framework, and speeds up the training of RFs by 7.8x on average when compared to state-of-the-art RF solvers (sklearn, H2O, and xgboost) on a range of datasets, RF configurations, and multi-core CPU architectures.

Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution $p$ and the generator distribution $p_G$. It implies that the trained discriminator can approximate optimal transport (OT) from $p_G$ to $p$.Based on some experiments and a bit of OT theory, we propose a discriminator optimal transport (DOT) scheme to improve generated images. We show that it improves inception score and FID calculated by un-conditional GAN trained by CIFAR-10, STL-10 and a public pre-trained model of conditional GAN by ImageNet.

Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods. In this paper, we introduce REVE, a new regularization scheme. Noting that compressing the representation can be sub-optimal, our first contribution is to identify a variable that is directly responsible for the final prediction. Our method aims at compressing the class conditioned entropy of this latter variable. Second, we introduce a variational upper bound on this conditional entropy term. Finally, we propose a scheme to instantiate a tractable loss that is integrated within the training procedure of the neural network and demonstrate its efficiency on different neural networks and datasets.

All except the real data are augmented with synthetic targets using the method from [15] 3, examples of these are provided in Figure 1. 4) Experiment 2.1: Data shortage: for this experiment MC-pix2pix was trained on the available real training set (flat and non-complex). The MC-pix2pix-generated data were used to train the A TR, which then was tested on another flat and non-complex dataset. Table II (top) shows that MC-pix2pix provides significant improvements in MAP, compared to just real data and other baselines, and the best F1. 5) Experiment 2.2: Lack of complexity: in this case MC-pix2pix was pre-trained with slightly more complex ripply seabeds, emulating previous exposure to the complex data. It then generated more of the complex seabeds, that were used to train the A TR alongside the flat and non-complex real data. When testing this A TR on complex real terrains (results presented at the bottom of Table II), both F1-score and mAP drastically improve with the MC-pix2pix data bootstrapping, compared to just real data training and baselines. This confirms that MC-pix2pix could be deployed as a highly efficient bootstrapping technique for improving A TR performance in cases of low real data availability or low real data diversity, that are common in the real life applications.

Application of discrete-time survival methods for continuous-time survival prediction is considered. For this purpose, a scheme for discretization of continuous-time data is proposed by considering the quantiles of the estimated event-time distribution, and, for smaller data sets, it is found to be preferable over the commonly used equidistant scheme. Furthermore, two interpolation schemes for continuous-time survival estimates are explored, both of which are shown to yield improved performance compared to the discrete-time estimates. The survival methods considered are based on the likelihood for right-censored survival data, and parameterize either the probability mass function (PMF) or the discrete-time hazard rate, both with neural networks. Through simulations and study of real-world data, the hazard rate parametrization is found to perform slightly better than the parametrization of the PMF. Inspired by these investigations, a continuous-time method is proposed by assuming that the continuous-time hazard rate is piecewise constant. The method, named PC-Hazard, is found to be highly competitive with the aforementioned methods in addition to other methods for survival prediction found in the literature.

Navigating complex urban environments safely is a key to realize fully autonomous systems. Predicting future locations of vulnerable road users, such as pedestrians and cyclists, thus, has received a lot of attention in the recent years. While previous works have addressed modeling interactions with the static (obstacles) and dynamic (humans) environment agents, we address an important gap in trajectory prediction. We propose SafeCritic, a model that synergizes generative adversarial networks for generating multiple "real" trajectories with reinforcement learning to generate "safe" trajectories. The Discriminator evaluates the generated candidates on whether they are consistent with the observed inputs. The Critic network is environmentally aware to prune trajectories that are in collision or are in violation with the environment. The auto-encoding loss stabilizes training and prevents mode-collapse. We demonstrate results on two large scale data sets with a considerable improvement over state-of-the-art. We also show that the Critic is able to classify the safety of trajectories.