UAI 2021 Papers

Creating representations of shapes that are invariant to isometric or almost-isometric transformations has long been an area of interest in shape analysis, since enforcing invariance allows the learning of more effective and robust shape representations. Most existing invariant shape representations are handcrafted, and previous work on learning shape representations do not focus on producing invariant representations. To solve the problem of learning unsupervised invariant shape representations, we use contrastive learning, which produces discriminative representations through learning invariance to user-specified data augmentations. To produce representations that are specifically isometry and almost-isometry invariant, we propose new data augmentations that randomly sample these transformations. We show experimentally that our method outperforms previous unsupervised learning approaches in both effectiveness and robustness.

Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being generated by an explicit adversary, while the poor train–test generalization of adversarial metrics can limit their usage to simple problems. Motivated by this, we develop a probabilistic robust risk framework, the statistically robust risk (SRR), which considers pointwise corruption distributions, as opposed to worst-case adversaries. The SRR provides a distinct and complementary measure of robust performance, compared to natural and adversarial risk. We show that the SRR admits estimation and training schemes which are as simple and efficient as for the natural risk: these simply require noising the inputs, but with a principled derivation for exactly how and why this should be done. Furthermore, we demonstrate both theoretically and experimentally that it can provide superior generalization performance compared with adversarial risks, enabling application to high-dimensional datasets.

Deep learning architectures with a huge number of parameters are often compressed using

A butterfly network consists of logarithmically many layers, each with a linear number of non-zero weights (pre-specified). The fast Johnson-Lindenstrauss transform (FJLT) can be represented as a butterfly network followed by a projection onto a random subset of the coordinates. Moreover, a random matrix based on FJLT with high probability approximates the action of any matrix on a vector. Motivated by these facts, we propose to replace a dense linear layer in any neural network by an architecture based on the butterfly network. The proposed architecture significantly improves upon the quadratic number of weights required in a standard dense layer to nearly linear with little compromise in expressibility of the resulting operator. In a collection of wide variety of experiments, including supervised prediction on both the NLP and vision data, we show that this not only produces results that match and at times outperform existing well-known architectures, but it also offers faster training and prediction in deployment. To understand the optimization problems posed by neural networks with a butterfly network, we also study the optimization landscape of the encoder-decoder network, where the encoder is replaced by a butterfly network followed by a dense linear layer in smaller dimension. Theoretical result presented in the paper explains why the training speed and outcome are not compromised by our proposed approach.

In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and accurately. Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature for OoD Detection (SCOD), an architecture-agnostic framework for equipping any trained DNN with a task-relevant epistemic uncertainty estimate. Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix which characterizes which directions in the weight space are most influential on the predictions over the training data. Online, we estimate uncertainty by measuring how much perturbations orthogonal to these directions can alter predictions at a new test input. We apply SCOD to pre-trained networks of varying architectures on several tasks, ranging from regression to classification. We demonstrate that SCOD achieves comparable of better OoD detection performance with lower computational burden relative to existing baselines.

We consider the stochastic combinatorial semi-bandit problem with adversarial corruptions. We provide a simple combinatorial algorithm that can achieve a regret of $\tilde{O}\left(C+d^2K/\Delta_{min}\right)$ where $C$ is the total amount of corruptions, $d$ is the maximal number of arms one can play in each round, $K$ is the number of arms. If one selects only one arm in each round, we achieves a regret of $\tilde{O}\left(C+\sum_{\Delta_i>0}(1/\Delta_i)\right)$. Our algorithm is combinatorial and improves on the previous combinatorial algorithm by [Gupta et al., COLT2019] (their bound is $\tilde{O}\left(KC+\sum_{\Delta_i>0}(1/\Delta_i)\right)$), and almost matches the best known bounds obtained by [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] (up to logarithmic factor). Note that the algorithms in [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] require one to solve complex convex programs while our algorithm is combinatorial, very easy to implement, requires weaker assumptions and has very low oracle complexity and running time. We also study the setting where we only get access to an approximation oracle for the stochastic combinatorial semi-bandit problem. Our algorithm achieves an (approximation) regret bound of $\tilde{O}\left(d\sqrt{KT}\right)$. Our algorithm is very simple, only worse than the best known regret bound by $\sqrt{d}$, and has much lower oracle complexity than previous work.

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in sparse time series, such as those found in various biological settings, e.g., gene transcriptomics. We show that the GP measure is equivalent to the Euclidean distance when the noise variance in the GP is negligible compared to the noise variance of the signal. Our numerical experiments on both synthetic and real data show improved performance of the GP similarity when used in conjunction with two distance-based clustering methods.

Sequential Monte Carlo (SMC) is a general-purpose methodology for recursive Bayesian inference, and is widely used in state space modeling and probabilistic programming. Its resample-move variant reduces the variance of posterior estimates by interleaving Markov chain Monte Carlo (MCMC) steps for particle “rejuvenation”; but this requires accessing all past observations and leads to linearly growing memory size and quadratic computation cost. Under the assumption of exchangeability, we introduce sequential core-set Monte Carlo (SCMC), which achieves constant space and linear time by rejuvenating based on sparse, weighted subsets of past data. In contrast to earlier approaches, which uniformly subsample or throw away observations, SCMC uses a novel online version of a state-of-the-art Bayesian core-set algorithm to incrementally construct a nonparametric, data- and model-dependent variational representation of the unnormalized target density. Experiments demonstrate significantly reduced approximation errors at negligible additional cost.

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach that exhibits favourable exploration properties in high-dimensional models such as neural networks. Unfortunately, HMC has limited use in large-data regimes and little work has explored suitable approaches that aim to preserve the entire Hamiltonian. In our work, we introduce a new symmetric integration scheme for split HMC that does not rely on stochastic gradients. We show that our new formulation is more efficient than previous approaches and is easy to implement with a single GPU. As a result, we are able to perform full HMC over common deep learning architectures using entire data sets. In addition, when we compare with stochastic gradient MCMC, we show that our method achieves better performance in both accuracy and uncertainty quantification. Our approach demonstrates HMC as a feasible option when considering inference schemes for large-scale machine learning problems.

In this paper, we consider constrained optimization problems subject to a convex set C Stochastic gradient descent (SGD) is a simple and popular stochastic optimization algorithm that has been the workhorse of machine learning for many years. We show a new and surprising fact about SGD, in that depending on the constraint set C, one can operate SGD with much lower-dimensional stochastic gradients without affecting its performance. In particular, we design an optimization algorithm that operates with the lower-dimensional (compressed) stochastic gradients, and establish that with the right set of parameters it has the exact same dimension-free convergence guarantees as that of regular SGD for popular convex and nonconvex optimization settings. We also present two applications of these bounds, one for improving the empirical risk minimization bounds in differentially private nonconvex optimization, and other for reducing communication costs with distributed SGD. Additionally, we also show that this connection between constraint set structure and gradient compression also extends beyond SGD to the conditional gradient (Frank-Wolfe) method. The geometry of the constraint set, captured by its Gaussian width, plays an important role in all our results.

Zero-Shot Learning (ZSL) is a classification task where some classes referred to as

Green security domains feature defenders who plan patrols in the face of uncertainty about the adversarial behavior of poachers, illegal loggers, and illegal fishers. Importantly, the deterrence effect of patrols on adversaries’ future behavior makes patrol planning a sequential decision-making problem. Therefore, we focus on robust sequential patrol planning for green security following the minimax regret criterion, which has not been considered in the literature. We formulate the problem as a game between the defender and nature who controls the parameter values of the adversarial behavior and design an algorithm MIRROR to find a robust policy. MIRROR uses two reinforcement learning–based oracles and solves a restricted game considering limited defender strategies and parameter values. We evaluate MIRROR on real-world poaching data.

It has long been known that principal component analysis (PCA) is not robust with respect to gross data corruption. This has been addressed by robust principal component analysis (RPCA). The first computationally tractable definition of RPCA decomposes a data matrix into a low-rank and a sparse component. The low-rank component represents the principal components, while the sparse component accounts for the data corruption. Previous works consider the corruption of individual entries or whole columns of the data matrix. In contrast, we consider a more general form of data corruption that affects groups of measurements. We show that the decomposition approach remains computationally tractable and allows the exact recovery of the decomposition when only the corrupted data matrix is given. Experiments on synthetic data corroborate our theoretical findings, and experiments on several real-world datasets from different domains demonstrate the wide applicability of our generalized approach.

We design a new efficient strategy synthesis method applicable to adversarial patrolling problems on graphs with arbitrary-length edges and possibly imperfect intrusion detection. The core ingredient is an efficient algorithm for computing the value and the gradient of a function assigning to every strategy its “protection” achieved. This allows for designing an efficient strategy improvement algorithm by differentiable programming and optimization techniques. Our method is the first one applicable to real-world patrolling graphs of reasonable sizes. It outperforms the state-of-the-art strategy synthesis algorithm by a margin.

Deep networks often suffer from vanishing or exploding gradients due to inefficient signal propagation, leading to long training times or convergence difficulties. Various architecture designs, sophisticated residual-style networks, and initialization schemes have been shown to improve deep signal propagation. Recently, Pennington et al. [2017] used free probability theory to show that dynamical isometry plays an integral role in efficient deep learning. We show that the simplest architecture change of gating each residual connection using a single zero-initialized parameter satisfies initial dynamical isometry and outperforms more complex approaches. Although much simpler than its predecessors, this gate enables training thousands of fully connected layers with fast convergence and better test performance for ResNets trained on an image recognition task. We apply this technique to language modeling and find that we can easily train 120-layer Transformers. When applied to 12 layer Transformers, it converges 56% faster.

Density estimation could be viewed as a core component in machine learning, since a good estimator could be used to solve many tasks such as classification, regression, and imputing missing values. The main challenge of density estimation is balancing the model expressiveness and its learning and inference complexity. Probabilistic circuits (PCs) model a probability distribution as a computational graph. By imposing specific structural properties on such models many inference tasks become tractable. However, learning PCs usually relies on greedy and time consuming procedures. In this paper we propose a new unified approach to efficiently learn PCs having several structural properties. We introduce extremely randomized PCs (XPCs), PCs with a random structure. We show their advantage on standard density estimation benchmarks when compared to other density estimators.

In this paper, we propose deep architectures for learning instance specific abstain (reject option) binary classifiers. The proposed approach uses double sigmoid loss function as described by Kulin Shah and Naresh Manwani in ("Online Active Learning of Reject Option Classifiers", AAAI, 2020), as a performance measure. We show that the double sigmoid loss is classification calibrated. We also show that the excess risk of 0-d-1 loss is upper bounded by the excess risk of double sigmoid loss. We derive the generalization error bounds for the proposed architecture for reject option classifiers. To show the effectiveness of the proposed approach, we experiment with several real world datasets. We observe that the proposed approach not only performs comparable to the state-of-the-art approaches, it is also robust against label noise. We also provide visualizations to observe the important features learned by the network corresponding to the abstaining decision.

The Conference on Uncertainty in Artificial Intelligence (UAI) is a premier international conference on research related to representation, inference, learning and decision making in the presence of uncertainty within the field of Artificial Intelligence. This volume contains all papers that were accepted for the Thirty-seventh UAI Conference, held Online from July 27 to 30, 2021.

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