In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, collecting a large number of labeled data is known as a hard task, and most of the existing work pay little attention to the generalization ability with insufficient samples. Meanwhile, recent progress in large margin theory discloses that rather than just maximizing the minimum margin, both the margin mean and variance, which characterize the margin distribution, are more crucial to the overall generalization performance. To address the issue of insufficient training samples, we propose a margin distribution learning paradigm for ordinal embedding, entitled Distributional Margin based Ordinal Embedding (\textit{DMOE}). Precisely, we first define the margin for ordinal embedding problem. Secondly, we formulate a concise objective function which avoids maximizing margin mean and minimizing margin variance directly but exhibits the similar effect. Moreover, an Augmented Lagrange Multiplier based algorithm is customized to seek the optimal solution of \textit{DMOE} effectively. Experimental studies on both simulated and real-world datasets are provided to show the effectiveness of the proposed algorithm.

Despite the considerable success of convolutional neural networks in a broad array of domains, recent research has shown these to be vulnerable to small adversarial perturbations, commonly known as adversarial examples. Moreover, such examples have shown to be remarkably portable, or transferable, from one model to another, enabling highly successful black-box attacks. We explore this issue of transferability and robustness from two dimensions: first, considering the impact of conventional $l_p$ regularization as well as replacing the top layer with a linear support vector machine (SVM), and second, the value of combining regularized models into an ensemble. We show that models trained with different regularizers present barriers to transferability, as does partial information about the models comprising the ensemble.

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability.

A rigorous empirical comparison of two stochastic solvers is important when one of the solvers is a prototype of a new algorithm such as multiwalk (MWA). When searching for global minima in $\mathbb{R}^p$, the key data structures of MWA include: $p$ rulers with each ruler assigned $m$ marks and a set of $p$ neighborhood matrices of size up to $m(m-2)$, where each entry represents absolute values of pairwise differences between $m$ marks. Before taking the next step, a controller links the tableau of neighborhood matrices and computes new and improved positions for each of the $m$ marks. The number of columns in each neighborhood matrix is denoted as the neighborhood radius $r_n \le m-2$. Any variant of the DEA (differential evolution algorithm) has an effective population neighborhood of radius not larger than 1. Uncensored first-passage-time performance experiments that vary the neighborhood radius of a MW-solver can thus be readily compared to existing variants of DE-solvers. The paper considers seven test cases of increasing complexity and demonstrates, under uncensored first-passage-time performance experiments: (1) significant variability in convergence rate for seven DE-based solver configurations, and (2) consistent, monotonic, and significantly faster rate of convergence for the MW-solver prototype as we increase the neighborhood radius from 4 to its maximum value.

REINFORCEMENT LEARNING RL aims to optimize the behavior of agents that interact with an environment by taking actions in order to minimize a loss. An agent in a state s P S, takes an action a P A according to some policy π. After taking an action, the agent receives a perexample lossl. The expected per-example loss given a state and an action is denoted by Lps, aq, i.e., Lps, aq " E rl s, as. L is assumed to be unknown, and the aim of the agent is to find a policy which minimizes the per-example loss. During the agent's training, the policy π is usually chosen to be stochastic, i.e., πp sq is a probability distribution over the action space A conditional on a state s. Using a stochastic policy enables exploration of the agent's environment, which is fundamental in RL. Indeed, training in RL is similar to a tryand-fail process:the agent takes an action chosen according to its state, and afterwards improves its policy according to the loss received from the environment. Using a stochastic policy, the agent aims to minimize the loss Jps, πq, defined as ż Jps, πq " πpa sqLps, aq da.

Machine learning is one modern innovation that has helped man enhance not only many industrial and professional processes but also advances everyday living. But what is machine learning? It is a subset of artificial intelligence, which focuses on using statistical techniques to build intelligent computer systems in order to learn from databases available to it. Currently, machine learning has been used in multiple fields and industries. The intelligent systems built on machine learning algorithms have the capability to learn from past experience or historical data.

Abstract--Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.) and edges characterize the relationships between these primitives. However, these non-vectorial graph data cannot be straightforwardly plugged into off-the-shelf machine learning algorithms without a preliminary step of - explicit/implicit - graph vectorization and embedding. This embedding process should be resilient to intra-class graph variations while being highly discriminant. In this paper, we propose a novel high-order stochastic graphlet embedding (SGE) that maps graphs into vector spaces. Our main contribution includes a new stochastic search procedure that efficiently parses a given graph and extracts/samples unlimitedly high-order graphlets. We consider these graphlets, with increasing orders, to model local primitives as well as their increasingly complex interactions. In order to build our graph representation, we measure the distribution ofthese graphlets into a given graph, using particular hash functions that efficiently assign sampled graphlets into isomorphic sets with a very low probability of collision. When combined with maximum margin classifiers, these graphlet-based representations have positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases. I. INTRODUCTION In this paper, we consider the problem of graph-based classification: given a pattern (image, shape, handwritten character, documentetc.) Most of the early pattern classification methods were designed using numerical feature vectors resulting from statistical analysis [12], [29]. Other more successful extensions of these methods also integrate structural information (see for instance [27]). These extensions were built upon the assumption that parts, in patterns, do not appear independently and structural relationships among these parts are crucial in order to achieve effective description and classification [20].

This paper addresses the problem of evaluating learning systems in safety critical domains such as autonomous driving, where failures can have catastrophic consequences. We focus on two problems: searching for scenarios when learned agents fail and assessing their probability of failure. The standard method for agent evaluation in reinforcement learning, Vanilla Monte Carlo, can miss failures entirely, leading to the deployment of unsafe agents. We demonstrate this is an issue for current agents, where even matching the compute used for training is sometimes insufficient for evaluation. To address this shortcoming, we draw upon the rare event probability estimation literature and propose an adversarial evaluation approach. Our approach focuses evaluation on adversarially chosen situations, while still providing unbiased estimates of failure probabilities. The key difficulty is in identifying these adversarial situations -- since failures are rare there is little signal to drive optimization. To solve this we propose a continuation approach that learns failure modes in related but less robust agents. Our approach also allows reuse of data already collected for training the agent. We demonstrate the efficacy of adversarial evaluation on two standard domains: humanoid control and simulated driving. Experimental results show that our methods can find catastrophic failures and estimate failures rates of agents multiple orders of magnitude faster than standard evaluation schemes, in minutes to hours rather than days.

A vine copula model is a flexible high-dimensional dependence model which uses only bivariate building blocks. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. In this work, we formulate a vine structure learning problem with both vector and reinforcement learning representation. We use neural network to find the embeddings for the best possible vine model and generate a structure. Throughout experiments on synthetic and real-world datasets, we show that our proposed approach fits the data better in terms of log-likelihood. Moreover, we demonstrate that the model is able to generate high-quality samples in a variety of applications, making it a good candidate for synthetic data generation.

Compressive learning is a framework where (so far unsupervised) learning tasks use not the entire dataset but a compressed summary (sketch) of it. We propose a compressive learning classification method, and a novel sketch function for images.