Differentially Private Empirical Risk Minimization with Sparsity-Inducing Norms

Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they are often non-differentiable. We analyze the standard differentially private algorithms, such as output perturbation, Frank-Wolfe and objective perturbation. Output perturbation is a differentially private algorithm that is known to perform well for minimizing risks that are strongly convex. Previous works have derived excess risk bounds that are independent of the dimensionality. In this paper, we assume a particular class of convex but non-smooth regularizers that induce structured sparsity and loss functions for generalized linear models. We also consider differentially private Frank-Wolfe algorithms to optimize the dual of the risk minimization problem. We derive excess risk bounds for both these algorithms. Both the bounds depend on the Gaussian width of the unit ball of the dual norm. We also show that objective perturbation of the risk minimization problems is equivalent to the output perturbation of a dual optimization problem. This is the first work that analyzes the dual optimization problems of risk minimization problems in the context of differential privacy

Meta reinforcement learning with latent variable Gaussian processes

Learning from small data sets is critical in many practical applications where data collection is time consuming or expensive, e.g., robotics, animal experiments or drug design. Meta learning is one way to increase the data efficiency of learning algorithms by generalizing learned concepts from a set of training tasks to unseen, but related, tasks. Often, this relationship between tasks is hard coded or relies in some other way on human expertise. In this paper, we frame meta learning as a hierarchical latent variable model and infer the relationship between tasks automatically from data. We apply our framework in a modelbased reinforcement learning setting and show that our meta-learning model effectively generalizes to novel tasks by identifying how new tasks relate to prior ones from minimal data. This results in up to a 60% reduction in the average interaction time needed to solve tasks compared to strong baselines

Deep Reinforcement Learning: A Brief Survey

Deep reinforcement learning (DRL) is poised to revolutionize the field of artificial intelligence (AI) and represents a step toward building autonomous systems with a higher-level understanding of the visual world. Currently, deep learning is enabling reinforcement learning (RL) to scale to problems that were previously intractable, such as learning to play video games directly from pixels. DRL algorithms are also applied to robotics, allowing control policies for robots to be learned directly from camera inputs in the real world. In this survey, we begin with an introduction to the general field of RL, then progress to the main streams of value-based and policy-based methods. Our survey will cover central algorithms in deep RL, including the deep Q-network (DQN), trust region policy optimization (TRPO), and asynchronous advantage actor critic. In parallel, we highlight the unique advantages of deep neural networks, focusing on visual understanding via RL. To conclude, we describe several current areas of research within the field

A brief survey of deep reinforcement learning

Deep reinforcement learning (DRL) is poised to revolutionize the field of artificial intelligence (AI) and represents a step toward building autonomous systems with a higherlevel understanding of the visual world. Currently, deep learning is enabling reinforcement learning (RL) to scale to problems that were previously intractable, such as learning to play video games directly from pixels. DRL algorithms are also applied to robotics, allowing control policies for robots to be learned directly from camera inputs in the real world. In this survey, we begin with an introduction to the general field of RL, then progress to the main streams of value-based and policy-based methods. Our survey will cover central algorithms in deep RL, including the deep Q-network (DQN), trust region policy optimization (TRPO), and asynchronous advantage actor critic. In parallel, we highlight the unique advantages of deep neural networks, focusing on visual understanding via RL. To conclude, we describe several current areas of research within the field

Variational Integrator Networks for Physically Meaningful Embeddings

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose variational integrator networks, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded

The Graph Cut Kernel for Ranked Data

Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the preference is only known for a subset of all objects. For these reasons, state-of-the-art methods cannot scale to real-world applications, such as recommender systems. We address this challenge by exploiting the geometric structure of ranked data and additional available information about the objects to derive a kernel for ranking based on the graph cut function. The graph cut kernel combines the efficiency of submodular optimization with the theoretical properties of kernel-based methods. The graph cut kernel combines the efficiency of submodular optimization with the theoretical properties of kernel-based methods

Sliced Multi-Marginal Optimal Transport

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability in the number of measures, samples and dimensionality. In this work, we propose a multi-marginal optimal transport paradigm based on random one-dimensional projections, whose (generalized) distance we term the sliced multi-marginal Wasserstein distance. To construct this distance, we introduce a characterization of the one-dimensional multi-marginal Kantorovich problem and use it to highlight a number of properties of the sliced multi-marginal Wasserstein distance. In particular, we show that (i) the sliced multi-marginal Wasserstein distance is a (generalized) metric that induces the same topology as the standard Wasserstein distance, (ii) it admits a dimension-free sample complexity, (iii) it is tightly connected with the problem of barycentric averaging under the sliced-Wasserstein metric. We conclude by illustrating the sliced multi-marginal Wasserstein on multi-task density estimation and multi-dynamics reinforcement learning problems

Rare germline variants in DNA repair genes and the angiogenesis pathway predispose prostate cancer patients to develop metastatic disease

Background Prostate cancer (PrCa) demonstrates a heterogeneous clinical presentation ranging from largely indolent to lethal. We sought to identify a signature of rare inherited variants that distinguishes between these two extreme phenotypes. Methods We sequenced germline whole exomes from 139 aggressive (metastatic, age of diagnosis < 60) and 141 non-aggressive (low clinical grade, age of diagnosis ≥60) PrCa cases. We conducted rare variant association analyses at gene and gene set levels using SKAT and Bayesian risk index techniques. GO term enrichment analysis was performed for genes with the highest differential burden of rare disruptive variants. Results Protein truncating variants (PTVs) in specific DNA repair genes were significantly overrepresented among patients with the aggressive phenotype, with BRCA2, ATM and NBN the most frequently mutated genes. Differential burden of rare variants was identified between metastatic and non-aggressive cases for several genes implicated in angiogenesis, conferring both deleterious and protective effects. Conclusions Inherited PTVs in several DNA repair genes distinguish aggressive from non-aggressive PrCa cases. Furthermore, inherited variants in genes with roles in angiogenesis may be potential predictors for risk of metastases. If validated in a larger dataset, these findings have potential for future clinical application

Ribosomal RNA of Hyacinthus orientalis L. female gametophyte cells before and after fertilization

The nucleolar activity of Hyacinthus orientalis L. embryo sac cells was investigated. The distributions of nascent pre-rRNA (ITS1), 26S rRNA and of the 5S rRNA and U3 snoRNA were determined using fluorescence in situ hybridization (FISH). Our results indicated the different rRNA metabolism of the H. orientalis female gametophyte cells before and after fertilization. In the target cells for the male gamete, i.e., the egg cell and the central cell whose activity is silenced in the mature embryo sac (Pięciński et al. in Sex Plant Reprod 21:247–257, 2008; Niedojadło et al. in Planta doi:10.1007/s00425-012-1599-9, 2011), rRNA metabolism is directed at the accumulation of rRNPs in the cytoplasm and immature transcripts in the nucleolus. In both cells, fertilization initiates the maturation of the maternal pre-rRNA and the expression of zygotic rDNA. The resumption of rRNA transcription observed in the hyacinth zygote indicates that in plants, there is a different mechanism for the regulation of RNA Pol I activity than in animals. In synergids and antipodal cells, which have somatic functions, the nucleolar activity is correlated with the metabolic activity of these cells and changes in successive stages of embryo sac development