Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning

We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for training EBM, by replacing Markov Chain Monte Carlo (MCMC) distribution with a trainable sampler, such as a diffusion model. In GCD, the joint training of EBM and a diffusion model is formulated as a minimax problem, which reaches an equilibrium when both models converge to the data distribution. The minimax learning with GCD bears interesting equivalence to inverse reinforcement learning, where the energy corresponds to a negative reward, the diffusion model is a policy, and the real data is expert demonstrations. We present preliminary yet promising results showing that joint training is beneficial for both EBM and a diffusion model. GCD enables EBM training without MCMC while improving the sample quality of a diffusion model.

Variational Weighting for Kernel Density Ratios

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias in standard kernel density estimates for density ratios, leading to improved estimates of prediction posteriors and information-theoretic measures. In the process, we shed light on some fundamental aspects of density estimation, particularly from the perspective of algorithms that employ KDEs as their main building blocks.

Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point along a low-dimensional manifold that approximates the training dataset. Then, EBM is trained to maximize the probability of recovering the original data. The training involves the generation of negative samples via MCMC, as in conventional EBM training, but from a different distribution concentrated near the manifold. The resulting near-manifold negative samples are highly informative, reflecting relevant modes of variation in data. An energy function of MPDR effectively learns accurate boundaries of the training data distribution and excels at detecting out-of-distribution samples. Experimental results show that MPDR exhibits strong performance across various anomaly detection tasks involving diverse data types, such as images, vectors, and acoustic signals.

Local Metric Learning for Off-Policy Evaluation in Contextual Bandits with Continuous Actions

We consider local kernel metric learning for off-policy evaluation (OPE) of deterministic policies in contextual bandits with continuous action spaces. Our work is motivated by practical scenarios where the target policy needs to be deterministic due to domain requirements, such as prescription of treatment dosage and duration in medicine. Although importance sampling (IS) provides a basic principle for OPE, it is ill-posed for the deterministic target policy with continuous actions. Our main idea is to relax the target policy and pose the problem as kernel-based estimation, where we learn the kernel metric in order to minimize the overall mean squared error (MSE). We present an analytic solution for the optimal metric, based on the analysis of bias and variance. Whereas prior work has been limited to scalar action spaces or kernel bandwidth selection, our work takes a step further being capable of vector action spaces and metric optimization. We show that our estimator is consistent, and significantly reduces the MSE compared to baseline OPE methods through experiments on various domains.

Evaluating Out-of-Distribution Detectors Through Adversarial Generation of Outliers

A reliable evaluation method is essential for building a robust out-of-distribution (OOD) detector. Current robustness evaluation protocols for OOD detectors rely on injecting perturbations to outlier data. However, the perturbations are unlikely to occur naturally or not relevant to the content of data, providing a limited assessment of robustness. In this paper, we propose Evaluation-via-Generation for OOD detectors (EvG), a new protocol for investigating the robustness of OOD detectors under more realistic modes of variation in outliers. EvG utilizes a generative model to synthesize plausible outliers, and employs MCMC sampling to find outliers misclassified as in-distribution with the highest confidence by a detector. We perform a comprehensive benchmark comparison of the performance of state-of-the-art OOD detectors using EvG, uncovering previously overlooked weaknesses.

Autoencoding Under Normalization Constraints

Likelihood is a standard estimate for outlier detection. The specific role of the normalization constraint is to ensure that the out-of-distribution (OOD) regime has a small likelihood when samples are learned using maximum likelihood. Because autoencoders do not possess such a process of normalization, they often fail to recognize outliers even when they are obviously OOD. We propose the Normalized Autoencoder (NAE), a normalized probabilistic model constructed from an autoencoder. The probability density of NAE is defined using the reconstruction error of an autoencoder, which is differently defined in the conventional energy-based model. In our model, normalization is enforced by suppressing the reconstruction of negative samples, significantly improving the outlier detection performance. Our experimental results confirm the efficacy of NAE, both in detecting outliers and in generating in-distribution samples.

Learning to increase matching efficiency in identifying additional b-jets in the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ process

The $\text{t}\bar{\text{t}}\text{H}(\text{b}\bar{\text{b}})$ process is an essential channel to reveal the Higgs properties but has an irreducible background from the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ process, which produces a top quark pair in association with a b quark pair. Therefore, understanding the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ process is crucial for improving the sensitivity of a search for the $\text{t}\bar{\text{t}}\text{H}(\text{b}\bar{\text{b}})$ process. To this end, when measuring the differential cross-section of the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ process, we need to distinguish the b-jets originated from top quark decays, and additional b-jets originated from gluon splitting. Since there are no simple identification rules, we adopt deep learning methods to learn from data to identify the additional b-jets from the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ events. Specifically, by exploiting the special structure of the $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ event data, we propose several loss functions that can be minimized to directly increase the matching efficiency, the accuracy of identifying additional b-jets. We discuss the difference between our method and another deep learning-based approach based on binary classification arXiv:1910.14535 using synthetic data. We then verify that additional b-jets can be identified more accurately by increasing matching efficiency directly rather than the binary classification accuracy, using simulated $\text{t}\bar{\text{t}}\text{b}\bar{\text{b}}$ event data in the lepton+jets channel from pp collision at $\sqrt{s}$ = 13 TeV.

K-Beam Minimax: Efficient Optimization for Deep Adversarial Learning

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new epsilon-subgradient descent algorithm that addresses this problem by simultaneously tracking K candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in K. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.

Nearest neighbor density functional estimation based on inverse Laplace transform

A general approach to $L_2$-consistent estimation of various density functionals using $k$-nearest neighbor distances is proposed, along with the analysis of convergence rates in mean squared error. The construction of the estimator is based on inverse Laplace transforms related to the target density functional, which arises naturally from the convergence of a normalized volume of $k$-nearest neighbor ball to a Gamma distribution in the sample limit. Some instantiations of the proposed estimator rediscover existing $k$-nearest neighbor based estimators of Shannon and Renyi entropies and Kullback--Leibler and Renyi divergences, and discover new consistent estimators for many other functionals, such as Jensen--Shannon divergence and generalized entropies and divergences. A unified finite-sample analysis of the proposed estimator is presented that builds on a recent result by Gao, Oh, and Viswanath (2017) on the finite sample behavior of the Kozachenko--Leoneko estimator of entropy.

Scalable Iterative Algorithm for Robust Subspace Clustering

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and SC, while most of them are computationally very expensive, in particular, for high dimensional large-scale data. In this paper, we develop much faster iterative algorithms for SC, incorporating robustness using a {\em non-squared} $\ell_2$-norm objective. The known implementations for optimizing the objective would be costly due to the alternative optimization of two separate objectives: optimal cluster-membership assignment and robust subspace selection, while the substitution of one process to a faster surrogate can cause failure in convergence. To address the issue, we use a simplified procedure requiring efficient matrix-vector multiplications for subspace update instead of solving an expensive eigenvector problem at each iteration, in addition to release nested robust PCA loops. We prove that the proposed algorithm monotonically converges to a local minimum with approximation guarantees, e.g., it achieves 2-approximation for the robust PCA objective. In our experiments, the proposed algorithm is shown to converge at an order of magnitude faster than known algorithms optimizing the same objective, and have outperforms prior subspace clustering methods in accuracy and running time for MNIST dataset.