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Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing points is generally not associated with uncertainty which prevents us from applying the apparatus of Bayesian reasoning for identifying an appropriate trade-off. In this work we place a point process prior on the inducing points and approximate the associated posterior through stochastic variational inference. By letting the prior encourage a moderate number of inducing points, we enable the model to learn which and how many points to utilise. We experimentally show that fewer inducing points are preferred by the model as the points become less informative, and further demonstrate how the method can be employed in deep Gaussian processes and latent variable modelling.


UAI 2021

Probabilistic Selection of Inducing Points in Sparse Gaussian Processes

bayesian hierarchical modelling

probabilistic pruning

sparse gaussian processes

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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

technical paper

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

The 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021) is held fully online. We have an exciting program consisting of keynote talks by [Susan Murphy](https://www.auai.org/uai2021/program?block=A), [Eric Horvitz](https://www.auai.org/uai2021/program?block=B), [Lenka Zdeborová](https://www.auai.org/uai2021/program?block=C), [Judea Pearl](https://www.auai.org/uai2021/program?block=D) and [Ankur Moitra](https://www.auai.org/uai2021/program?block=E), a town hall meeting, peer-reviewed papers, and three workshops. The main conference is single-track and each paper is show-cased with a live component (either a live discussion and Q&A, or a live lightning talk). All papers are also featured in video presentations and in poster sessions in gather.town. The three parallel workshops on Friday allow for smaller meetings on current topics.

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The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

Variational inference has had great success in scaling approximate Bayesian inference to big data by exploiting mini-batch training. To date, however, this strategy has been most applicable to models of independent data. We propose an extension to state space models of time series data based on a novel generative model for latent temporal states: the neural moving average model. This permits a subsequence to be sampled without drawing from the entire distribution, enabling training iterations to use mini-batches of the time series at low computational cost. We illustrate our method on autoregressive, Lotka-Volterra, FitzHugh-Nagumo and stochastic volatility models, achieving accurate parameter estimation in a short time.

The Neural Moving Average Model for Scalable Variational Inference of State Space Models

Batch Bayesian optimisation (BO) is a successful technique for the optimisation of expensive black-box functions. Asynchronous BO can reduce wallclock time by starting a new evaluation as soon as another finishes, thus maximising resource utilisation. To maximise resource allocation, we develop a novel asynchronous BO method, AEGiS (Asynchronous ε-Greedy Global Search) that combines greedy search, exploiting the surrogate's mean prediction, with Thompson sampling and random selection from the approximate Pareto set describing the trade-off between exploitation (surrogate mean prediction) and exploration (surrogate posterior variance). We demonstrate empirically the efficacy of AEGiS on synthetic benchmark problems, meta-surrogate hyperparameter tuning problems and real-world problems, showing that AEGiS generally outperforms existing methods for asynchronous BO. When a single worker is available performance is no worse than BO using expected improvement.



Asynchronous e-Greedy Bayesian Optimisation

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases.

Explaining Fast Improvement in Online Imitation Learning

Resource allocation for coverage of geographical spaces is a challenging problem in robotics, sensor networks and security domains. Conventional solution approaches either: (a) rely on exploiting spatio-temporal structure of specific coverage problems, or (b) use genetic algorithms when targeting general coverage problems where no special exploitable structure exists. In this work, we propose the coverage gradient theorem, which provides a gradient estimator for a broad class of spatial coverage objectives using a combination of Newton-Leibniz theorem and implicit boundary differentiation. We also propose a tractable framework to approximate the coverage objectives and their gradients using spatial discretization and empirically demonstrate the efficacy of our framework on multi-resource spatial coverage problems.

Gradient-based Optimization for Multi-resource Spatial Coverage 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.

E5 SGD with Low-Dimensional Gradients with Applications to Private and Distributed Learning

Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics.

Generalizing the Geometric Annealing Path using Power Means

An important achievement in the field of causal inference was a complete characterization of when a causal effect, in a system modeled by a causal graph, can be determined uniquely from purely observational data. The identification algorithms resulting from this work produce exact symbolic expressions for causal effects, in terms of the observational probabilities. More recent work has looked at the numerical properties of these expressions, in particular using the classical notion of the condition number. In its classical interpretation, the condition number quantifies the sensitivity of the output values of the expressions to small numerical perturbations in the input observational probabilities. In the context of causal identification, the condition number has also been shown to be related to the effect of certain kinds of uncertainties in the structure of the causal graphical model.

Condition Number Bounds for Causal Inference

Unsupervised multi-object scene decomposition is a fast-emerging problem in representation learning. Despite significant progress in static scenes, such models are unable to leverage important dynamic cues present in videos. We propose PROVIDE, a novel unsupervised framework for PRObabilistic VIdeo DEcomposition based on a temporal extension of iterative inference. PROVIDE is powerful enough to jointly model complex individual multi-object representations and explicit temporal dependencies between latent variables across frames. This is achieved by leveraging 2D-LSTM, temporally conditioned inference and generation within the iterative amortized inference for posterior refinement. Our method improves the overall quality of decompositions, encodes information about the objects' dynamics, and can be used to predict trajectories of each object separately. Additionally, we show that our model has a high accuracy even without color information. We demonstrate the decomposition capabilities of our model and show that it outperforms the state-of-the-art on several benchmark datasets, one of which was curated for this work and will be made publicly available.

PROVIDE: A Probabilistic Framework for Unsupervised Video Decomposition

Conditional independence (CI) is a fundamental concept with wide applications in machine learning and causal inference. Although the problems of testing CI and estimating divergences have been extensively studied, the complementary problem of generating data that satisfies CI has received much less attention. Given samples from an input data distribution, we formulate the problem of generating samples from a distribution that is close to the input distribution and satisfies CI. We establish a general characterization of CI in terms of a divergence identity that holds for a large class of divergences satisfying separability and strict convexity properties. Based on the Jensen-Shannon version of this identity, an architecture is proposed that leverages the capabilities of generative adversarial networks (GANs) to enforce CI in an end-to-end differentiable manner. As one illustration of the problem formulation and architecture, we consider applications to notions of fairness that can be written as enforcing CIs. We demonstrate the generation of data to trade off adherence to fairness criteria against classification accuracy.

Conditionally Independent Data Generation

We consider Bayesian inference problems where the likelihood function is either expensive to evaluate or only available via noisy estimates. This setting encompasses application scenarios involving, for example, large datasets or models whose likelihood evaluations require expensive simulations. We formulate this problem within a Bayesian optimisation framework over a space of probability distributions and derive an upper confidence bound (UCB) algorithm to propose non-parametric distribution candidates. The algorithm is designed to minimise regret, which is defined as the Kullback-Leibler divergence with respect to the true posterior in this case. Equipped with a Gaussian process surrogate model, we show that the resulting UCB algorithm achieves asymptotically no regret. The method can be easily implemented as a batch Bayesian optimisation algorithm whose point evaluations are selected via Markov chain Monte Carlo. Experimental results demonstrate the method's performance on inference problems.

Probabilistic Selection of Inducing Points in Sparse Gaussian Processes

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