| Total: 139
Domain adaptation in imitation learning represents an essential step towards improving generalizability. However, even in the restricted setting of third-person imitation where transfer is between isomorphic Markov Decision Processes, there are no strong guarantees on the performance of transferred policies. We present problem-dependent, statistical learning guarantees for third-person imitation from observation in an offline setting, and a lower bound on performance in the online setting.
Semi-supervised learning algorithms attempt to take advantage of relatively inexpensive unlabeled data to improve learning performance. In this work, we consider statistical models where the data distributions can be characterized by continuous parameters. We show that under certain conditions on the distribution, unlabeled data is equally useful as labeled date in terms of learning rate. Specifically, let $n, m$ be the number of labeled and unlabeled data, respectively. It is shown that the learning rate of semi-supervised learning scales as $O(1/n)$ if $m\sim n$, and scales as $O(1/n^{1+\gamma})$ if $m\sim n^{1+\gamma}$ for some $\gamma>0$, whereas the learning rate of supervised learning scales as $O(1/n)$.
Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set. Due to the infinity the latent features, posterior inference requires either marginalization—resulting in dependence structures that prevent efficient computation via parallelization and conjugacy—or finite truncation, which arbitrarily limits the flexibility of the model. In this paper we present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables, enabling efficient, parallelized computation without sacrificing flexibility. In contrast to past work that achieved this on a model-by-model basis, we provide a general recipe that is applicable to the broad class of completely random measure-based priors. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models, demonstrating a higher effective sample size per second compared to algorithms using marginalization as well as a higher predictive performance compared to models employing fixed truncations.
Collective learning methods exploit relations among data points to enhance classification performance. However, such relations, represented as edges in the underlying graphical model, expose an extra attack surface to the adversaries. We study adversarial robustness of an important class of such graphical models, Associative Markov Networks (AMN), to structural attacks, where an attacker can modify the graph structure at test time. We formulate the task of learning a robust AMN classifier as a bi-level program, where the inner problem is a challenging non- linear integer program that computes optimal structural changes to the AMN. To address this technical challenge, we first relax the attacker problem, and then use duality to obtain a convex quadratic upper bound for the robust AMN problem. We then prove a bound on the quality of the resulting approximately optimal solutions, and experimentally demonstrate the efficacy of our approach. Finally, we apply our approach in a transductive learning setting, and show that robust AMN is much more robust than state-of-the-art deep learning methods, while sacrificing little in accuracy on non-adversarial data.
This work proposes a novel momentum technique, the Amortized Nesterov’s Momentum, for stochastic convex optimization. The proposed method can be regarded as a smooth transition between Nesterov’s method and mirror descent. By tuning only a single parameter, users can trade Nesterov’s acceleration for robustness, that is, the variance control of the stochastic noise. Motivated by the recent success of using momentum in deep learning, we conducted extensive experiments to evaluate this new momentum in deep learning tasks. The results suggest that it can serve as a favorable alternative for Nesterov’s momentum.
Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.
Private data query combines mechanism design with privacy protection to produce aggregated statistics from privately-owned data records. The problem arises in a data marketplace where data owners have personalised privacy requirements and private data valuations. We focus on the case when the data owners are single-minded, i.e., they are willing to release their data only if the data broker guarantees to meet their announced privacy requirements. For a data broker who wants to purchase data from such data owners, we propose the SingleMindedQuery (SMQ) mechanism, which uses a reverse auction to select data owners and determine compensations. SMQ satisfies interim incentive compatibility, individual rationality, and budget feasibility. Moreover, it uses purchased privacy expectation maximisation as a principle to produce accurate outputs for commonly-used queries such as counting, median and linear predictor. The effectiveness of our method is empirically validated by a series of experiments.
Online learning in dynamic environments has recently drawn considerable attention, where dynamic regret is usually employed to compare decisions of online algorithms to dynamic comparators. In previous works, dynamic regret bounds are typically established in terms of regularity of comparators $C_T$ or that of online functions $V_T$. Recently, Jadbabaie et al. [2015] propose an algorithm that can take advantage of both regularities and enjoy an $\tilde{O}(\sqrt{1+D_T} + \min\{\sqrt{(1+D_T)C_T}, (1+D_T)^{1/3}V_T^{1/3}T^{1/3}\})$ dynamic regret, where $D_T$ is an additional quantity to measure the niceness of environments. The regret bound adapts to the smaller regularity of problem environments and is tighter than all existing dynamic regret guarantees. Nevertheless, their algorithm involves non-convex programming at each iteration, and thus requires burdensome computations. In this paper, we design a simple algorithm based on the online ensemble, which provably enjoys the same (even slightly stronger) guarantee as the state-of-the-art rate, yet is much more efficient because our algorithm does not involve any non-convex problem solving. Empirical studies also verify the efficacy and efficiency.
Semantic hashing has become a crucial component of fast similarity search in many large-scale information retrieval systems, in particular, for text data. Variational auto-encoders (VAEs) with binary latent variables as hashing codes provide state-of-the-art performance in terms of precision for document retrieval. We propose a pairwise loss function with discrete latent VAE to reward within-class similarity and between-class dissimilarity for supervised hashing. Instead of solving the optimization for training relying on existing biased gradient estimators, an unbiased, low-variance gradient estimator, which evaluates the non-differentiable loss function over two correlated sets of binary hashing codes to control the gradient variance, is adopted to optimize the hashing function to achieve superior performance compared to the state-of-the-arts, as demonstrated by our comprehensive experiments.
We derive and analyze learning algorithms for apprenticeship learning, policy evaluation and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on ideas from Markov chain theory and derive sampling algorithms that do not require such an upper bound. For these algorithms, we provide theoretical bounds on their sample-complexity and running time.
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the $k$-NN conditional mutual information estimator to the learned feature maps. The mappings are designed to ensure that mapped samples both preserve information and share similar information about the target variable if and only if they are close in Euclidean distance. We show that these properties boost the performance of the $k$-NN estimator in the second step. The performance of the proposed method is evaluated on both synthetic and real data.
We propose a novel probabilistic framework to model continuously generated interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the latent structure influence their interaction dynamics. To this end, we model the reciprocating interactions between individuals using mutually-exciting Hawkes processes. The base rate of the Hawkes process for each pair of individuals is built upon the latent representations inferred using the hierarchical gamma process edge partition model (HGaP-EPM). In particular, our model allows the interaction dynamics between each pair of individuals to be modulated by their respective affiliated communities.Moreover, our model can flexibly incorporate the auxiliary individuals’ attributes, or covariates associated with interaction events. Efficient Gibbs sampling and Expectation-Maximization algorithms are developed to perform inference via Pólya-Gamma data augmentation strategy. Experimental results on real-world datasets demonstrate that our model not only achieves competitive performance compared with state-of-the-art methods, but also discovers interpretable latent structure behind the observed temporal interactions.
We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting as optimization with dueling-choice bandits, since both direct queries and duels are available for optimization. We give the COMP-GP-UCB algorithm based on GP-UCB (Srinivas et al., 2009),, where instead of directly querying the point with the maximum Upper Confidence Bound (UCB), we perform constrained optimization and use comparisons to filter out suboptimal points. COMP-GP-UCB comes with theoretical guarantee of $O(\frac{\Phi}{\sqrt{T}})$ on simple regret where $T$ is the number of direct queries and $\Phi$ is an improved information gain stemming from a comparison-based constraint set that restricts the space for optimum search. In contrast, in the plain direct query setting, $\Phi$ depends on the entire domain. We discuss theoretical aspects and show experimental results to demonstrate efficacy of our algorithm.
Dominant generalized eigenspace computation, concerned with how to find one of the top-k generalized eigenspaces of a pair of real symmetric matrices, is one of the fundamental problems in scientific computing, data analysis, and statistics. In this work, we propose a practical Riemannian algorithm based on the first-order optimization on generalized Stiefel manifolds while efficiently leveraging second-order information. Particularly, we use inexact Riemannian gradients which result from running a fast least-squares solver to approximate matrix multiplications for avoiding costly matrix inversions involved therein. We also conduct a theoretical analysis that is different than existing ones, achieving a unified linear convergence rate regardless of the conventional generalized eigenvalue gap which is the key parameter to the currently dichotomized analysis: gap-dependent or gap-free. The resulting linear rate, albeit not optimal, remains valid in full generality. Despite the simplicity, empirically, our algorithm as a block generalized eigensolver remarkably outperforms existing solvers.
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of question by looking at performance averaged over data space, or otherwise lack diagnostic detail. However, if the approximation is bad for most data, but good at the observed data, then we may discard a useful approximation. We give graphical diagnostics for posterior approximation at the observed data. We estimate a “distortion map” that acts on univariate marginals of the approximate posterior to move them closer to the exact posterior, without recourse to the exact posterior.
Structured prediction of objects in spaces that are inherently difficult to search or compactly characterize is a particularly challenging task. For example, though bipartite matchings in two dimensions can be tractably optimized and learned, the higher-dimensional generalization—3D matchings—are NP-hard to optimally obtain and the set of potential solutions cannot be compactly characterized. Though approximation is therefore necessary, prevalent structured prediction methods inherit the weaknesses they possess in the two-dimensional setting either suffering from inconsistency or intractability—even when the approximations are sufficient. In this paper, we explore extending an adversarial approach to learning bipartite matchings that avoids these weaknesses to the three dimensional setting. We assess the benefits compared to margin-based methods on a three-frame tracking problem.
We prove performance guarantees of two algorithms for approximating Q* in batch reinforcement learning. Compared to classical iterative methods such as Fitted Q-Iteration—whose performance loss incurs quadratic dependence on horizon—these methods estimate (some forms of) the Bellman error and enjoy linear-in-horizon error propagation, a property established for the first time for algorithms that rely solely on batch data and output stationary policies. One of the algorithms uses a novel and explicit importance-weighting correction to overcome the infamous "double sampling" difficulty in Bellman error estimation, and does not use any squared losses. Our analyses reveal its distinct characteristics and potential advantages compared to classical algorithms.
We address the following question in this paper: “What are the most robust statistical methods for social choice?” By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and randomized tests, we characterize uniformly most powerful (UMP) tests, which is a well-accepted statistical optimality w.r.t. robustness, for testing whether a given alternative is the winner under Mallows’ model and under Condorcet’s model, respectively.
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq R^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.
Many classical algorithms output graphical representations of causal structures by testing conditional independence among a set of random variables. In dynamical systems, local independence can be used analogously as a testable implication of the underlying data-generating process. We suggest some inexpensive methods for causal screening which provide output with a sound causal interpretation under the assumption of ancestral faithfulness. The popular model class of linear Hawkes processes is used to provide an example of a dynamical causal model. We argue that for sparse causal graphs the output will often be close to complete. We give examples of this framework and apply it to a challenging biological system.
In this paper, we propose a novel optimization criterion that leverages features of the skew normal distribution to better model the problem of personalized recommendation. Specifically, the developed criterion borrows the concept and the flexibility of the skew normal distribution, based on which three hyperparameters are attached to the optimization criterion. Furthermore, from a theoretical point of view, we not only establish the relation between the maximization of the proposed criterion and the shape parameter in the skew normal distribution, but also provide the analogies and asymptotic analysis of the proposed criterion to maximization of the area under the ROC curve. Experimental results conducted on a range of large-scale real-world datasets show that our model significantly outperforms the state of the art and yields consistently best performance on all tested datasets.
Recent advances in variational auto-encoder (VAE) have demonstrated the possibility of approximating the intractable posterior distribution with a variational distribution parameterized by a neural network. To optimize the variational objective of VAE, the reparameterization trick is commonly applied to obtain a low-variance estimator of the gradient. The main idea of the trick is to express the variational distribution as a differentiable function of parameters and a random variable with a fixed distribution. To extend the reparameterization trick to inference involving discrete latent variables, a common approach is to use a continuous relaxation of the categorical distribution as the approximate posterior. However, when applying continuous relaxation to the multivariate cases, multiple variables are typically assumed to be independent, making it suboptimal in applications where modeling dependency is crucial to the overall performance. In this work, we propose a multivariate generalization of the Relaxed Bernoulli distribution, which can be reparameterized and can capture the correlation between variables via a Gaussian copula. We demonstrate its effectiveness in two tasks: density estimation with Bernoulli VAE and semi-supervised multi-label classification.
Greedy-GQ is an off-policy two timescale algorithm for optimal control in reinforcement learning. This paper develops the first finite-sample analysis for the Greedy-GQ algorithm with linear function approximation under Markovian noise. Our finite-sample analysis provides theoretical justification for choosing stepsizes for this two timescale algorithm for faster convergence in practice, and suggests a trade-off between the convergence rate and the quality of the obtained policy. Our paper extends the finite-sample analyses of two timescale reinforcement learning algorithms from policy evaluation to optimal control, which is of more practical interest. Specifically, in contrast to existing finite-sample analyses for two timescale methods, e.g., GTD, GTD2 and TDC, where their objective functions are convex, the objective function of the Greedy-GQ algorithm is non-convex. Moreover, the Greedy-GQ algorithm is also not a linear two-timescale stochastic approximation algorithm. Our techniques in this paper provide a general framework for finite-sample analysis of non-convex value-based reinforcement learning algorithms for optimal control.
Deep reinforcement learning (RL) algorithms have achieved great success on a wide variety of sequential decision-making tasks. However, many of these algorithms suffer from high sample complexity when learning from scratch using environmental rewards, due to issues such as credit-assignment and high-variance gradients, among others. Transfer learning, in which knowledge gained on a source task is applied to more efficiently learn a different but related target task, is a promising approach to improve the sample complexity in RL. Prior work has considered using pre-trained teacher policies to enhance the learning of the student policy, albeit with the constraint that the teacher and the student MDPs share the state-space or the action-space. In this paper, we propose a new framework for transfer learning where the teacher and the student can have arbitrarily different state- and action-spaces. To handle this mismatch, we produce embeddings which can systematically extract knowledge from the teacher policy and value networks, and blend it into the student networks. To train the embeddings, we use a task-aligned loss and show that the representations could be enriched further by adding a mutual information loss. Using a set of challenging simulated robotic locomotion tasks involving many-legged centipedes, we demonstrate successful transfer learning in situations when the teacher and student have different state- and action-spaces.
Bayesian inference of the Bayesian network structure requires averaging over all possible directed acyclic graphs, DAGs, each weighted by its posterior probability. For approximate averaging, the most popular method has been Markov chain Monte Carlo, MCMC. It was recently shown that collapsing the sampling space from DAGs to suitably defined ordered partitions of the nodes substantially expedites the chain’s convergence; this partition-MCMC is similar to order-MCMC on node orderings, but it avoids biasing the sampling distribution. Here, we further collapse the state space by merging some number of adjacent members of a partition into layers. This renders the computation of the (unnormalized) posterior probability of a state, called layering, more involved, for which task we give an efficient dynamic programming algorithm. Our empirical studies suggest that the resulting layering-MCMC is superior to partition-MCMC in terms of mixing time and estimation accuracy.