Long-Short Temporal Co-Teaching for Weakly Supervised Video Anomaly Detection

Weakly supervised video anomaly detection (WS-VAD) is a challenging problem that aims to learn VAD models only with video-level annotations. In this work, we propose a Long-Short Temporal Co-teaching (LSTC) method to address the WS-VAD problem. It constructs two tubelet-based spatio-temporal transformer networks to learn from short- and long-term video clips respectively. Each network is trained with respect to a multiple instance learning (MIL)-based ranking loss, together with a cross-entropy loss when clip-level pseudo labels are available. A co-teaching strategy is adopted to train the two networks. That is, clip-level pseudo labels generated from each network are used to supervise the other one at the next training round, and the two networks are learned alternatively and iteratively. Our proposed method is able to better deal with the anomalies with varying durations as well as subtle anomalies. Extensive experiments on three public datasets demonstrate that our method outperforms state-of-the-art WS-VAD methods.

Hierarchical Semantic Contrast for Scene-aware Video Anomaly Detection

Increasing scene-awareness is a key challenge in video anomaly detection (VAD). In this work, we propose a hierarchical semantic contrast (HSC) method to learn a scene-aware VAD model from normal videos. We first incorporate foreground object and background scene features with high-level semantics by taking advantage of pre-trained video parsing models. Then, building upon the autoencoder-based reconstruction framework, we introduce both scene-level and object-level contrastive learning to enforce the encoded latent features to be compact within the same semantic classes while being separable across different classes. This hierarchical semantic contrast strategy helps to deal with the diversity of normal patterns and also increases their discrimination ability. Moreover, for the sake of tackling rare normal activities, we design a skeleton-based motion augmentation to increase samples and refine the model further. Extensive experiments on three public datasets and scene-dependent mixture datasets validate the effectiveness of our proposed method.

Information-theoretic Online Memory Selection for Continual Learning

A challenging problem in task-free continual learning is the online selection of a representative replay memory from data streams. In this work, we investigate the online memory selection problem from an information-theoretic perspective. To gather the most information, we propose the \textit{surprise} and the \textit{learnability} criteria to pick informative points and to avoid outliers. We present a Bayesian model to compute the criteria efficiently by exploiting rank-one matrix structures. We demonstrate that these criteria encourage selecting informative points in a greedy algorithm for online memory selection. Furthermore, by identifying the importance of \textit{the timing to update the memory}, we introduce a stochastic information-theoretic reservoir sampler (InfoRS), which conducts sampling among selective points with high information. Compared to reservoir sampling, InfoRS demonstrates improved robustness against data imbalance. Finally, empirical performances over continual learning benchmarks manifest its efficiency and efficacy.

Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition

We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.

Beyond Marginal Uncertainty: How Accurately can Bayesian Regression Models Estimate Posterior Predictive Correlations?

While uncertainty estimation is a well-studied topic in deep learning, most such work focuses on marginal uncertainty estimates, i.e. the predictive mean and variance at individual input locations. But it is often more useful to estimate predictive correlations between the function values at different input locations. In this paper, we consider the problem of benchmarking how accurately Bayesian models can estimate predictive correlations. We first consider a downstream task which depends on posterior predictive correlations: transductive active learning (TAL). We find that TAL makes better use of models' uncertainty estimates than ordinary active learning, and recommend this as a benchmark for evaluating Bayesian models. Since TAL is too expensive and indirect to guide development of algorithms, we introduce two metrics which more directly evaluate the predictive correlations and which can be computed efficiently: meta-correlations (i.e. the correlations between the models correlation estimates and the true values), and cross-normalized likelihoods (XLL). We validate these metrics by demonstrating their consistency with TAL performance and obtain insights about the relative performance of current Bayesian neural net and Gaussian process models.

Fast-rate PAC-Bayes Generalization Bounds via Shifted Rademacher Processes

The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend this bridge between Rademacher complexity and state-of-the-art PAC-Bayesian theory. We first demonstrate that one can match the fast rate of Catoni's PAC-Bayes bounds (Catoni, 2007) using shifted Rademacher processes (Wegkamp, 2003; Lecu\'{e} and Mitchell, 2012; Zhivotovskiy and Hanneke, 2018). We then derive a new fast-rate PAC-Bayes bound in terms of the "flatness" of the empirical risk surface on which the posterior concentrates. Our analysis establishes a new framework for deriving fast-rate PAC-Bayes bounds and yields new insights on PAC-Bayesian theory.

Functional Variational Bayesian Neural Networks

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes equals the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors entailing rich structures, including Gaussian processes and implicit stochastic processes. Empirically, we find fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and scale to large datasets.

Differentiable Compositional Kernel Learning for Gaussian Processes

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN architecture is based on the composition rules for kernels, so that each unit of the network corresponds to a valid kernel. It can compactly approximate compositional kernel structures such as those used by the Automatic Statistician (Lloyd et al., 2014), but because the architecture is differentiable, it is end-to-end trainable with gradient-based optimization. We show that the NKN is universal for the class of stationary kernels. Empirically we demonstrate pattern discovery and extrapolation abilities of NKN on several tasks that depend crucially on identifying the underlying structure, including time series and texture extrapolation, as well as Bayesian optimization.

Aggregated Momentum: Stability Through Passive Damping

Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient $\beta$. Large $\beta$ values can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typically resorts to small values such as 0.5 or 0.9. We propose Aggregated Momentum (AggMo), a variant of momentum which combines multiple velocity vectors with different $\beta$ parameters. AggMo is trivial to implement, but significantly dampens oscillations, enabling it to remain stable even for aggressive $\beta$ values such as 0.999. We reinterpret Nesterov's accelerated gradient descent as a special case of AggMo and analyze rates of convergence for quadratic objectives. Empirically, we find that AggMo is a suitable drop-in replacement for other momentum methods, and frequently delivers faster convergence.

A Spectral Approach to Gradient Estimation for Implicit Distributions

Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's identity and a spectral decomposition of kernel operators, where the eigenfunctions are approximated by the Nystr\"om method. Unlike the previous works that only provide estimates at the sample points, our approach directly estimates the gradient function, thus allows for a simple and principled out-of-sample extension. We provide theoretical results on the error bound of the estimator and discuss the bias-variance tradeoff in practice. The effectiveness of our method is demonstrated by applications to gradient-free Hamiltonian Monte Carlo and variational inference with implicit distributions. Finally, we discuss the intuition behind the estimator by drawing connections between the Nystr\"om method and kernel PCA, which indicates that the estimator can automatically adapt to the geometry of the underlying distribution.