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Computing the expectation of kernel functions is a ubiquitous task in machine learning, with applications from classical support vector machines to exploiting kernel embeddings of distributions in probabilistic modeling, statistical inference, causal discovery, and deep learning. In all these scenarios, we tend to resort to Monte Carlo estimates as expectations of kernels are intractable in general. In this work, we characterize the conditions under which we can compute expected kernels exactly and efficiently, by leveraging recent advances in probabilistic circuit representations. We first construct a circuit representation for kernels and propose an approach to such tractable computation. We then demonstrate possible advancements for kernel embedding frameworks by exploiting tractable expected kernels to derive new algorithms for two challenging scenarios: 1) reasoning under missing data with kernel support vector regressors; 2) devising a collapsed black-box importance sampling scheme. Finally, we empirically evaluate both algorithms and show that they outperform standard baselines on a variety of datasets.

UAI 2021

Tractable Computation of Expected Kernels

exact inference

kernel methods

probabilistic circuits

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2021

lightning talk

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.

The walkthrough video below shows how you can navigate this site and use the different possibilities for interaction: UAIsland2021 on gather.town for posters and social interactions, the mementor platform for virtual mentoring sessions, and the chat and Q&A systems for discussions about talks and posters.

Have a great UAI 2021! 
<br>
<br>Cassio de Campos and Marloes Maathuis
<br>UAI 2021 Program Chairs
<br>uai2021programchairs@gmail.com

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A ticket is required to access this conference. Please use the provided link to register for the event.

https://auai.org/uai2021/registration

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/)

We propose probabilistic task modelling -- a generative probabilistic model for collections of tasks used in meta-learning. The proposed model combines variational auto-encoding and latent Dirichlet allocation to model each task as a mixture of Gaussian distribution in an embedding space. Such modelling provides an explicit representation of a task through its task-theme mixture. We present an efficient approximation inference technique based on variational inference method for empirical Bayes parameter estimation. We perform empirical evaluations to validate the task uncertainty and task distance produced by the proposed method through correlation diagrams of the prediction accuracy on testing tasks. We also carry out experiments of task selection in meta-learning to demonstrate how the task relatedness inferred from the proposed model help to facilitate meta-learning algorithms.

Probabilistic task modelling for meta-learning

This paper studies the relationship between generalization and privacy preservation of machine learning in two steps. We first establish an alignment between the two facets for any learning algorithm. We prove that $(\varepsilon, \delta)$-differential privacy implies an on-average generalization bound for a multi-sample-set learning algorithm, which further leads to a high-probability bound for any learning algorithm. We then investigate how the iterative nature shared by most learning algorithms influences privacy preservation and further generalization. Three composition theorems are proved to approximate the differential privacy of an iterative algorithm through the differential privacy of its every iteration. Integrating the above two steps, we eventually deliver generalization bounds for iterative learning algorithms. Our results are strictly tighter than the existing works. Particularly, our generalization bounds do not rely on the model size which is prohibitively large in deep learning. Experiments of MLP, VGG, and ResNet on MNIST, CIFAR-10, and CIFAR-100 are in full agreement with our theory. The theory applies to a wide spectrum of learning algorithms. In this paper, it is applied to the Gaussian mechanism as an example.

Tighter Generalization Bounds for Iterative Privacy-Preserving Algorithms

In the area of natural language processing, deep learning models are recently known to be vulnerable to various types of adversarial perturbations, but relatively few works are done on the defense side. Especially, there exists few effective defense method against the successful synonym substitution based attacks that preserve the syntactic structure and semantic information of the original text while fooling the deep learning models. We contribute in this direction and propose a novel adversarial defense method called Synonym Encoding Method (SEM). Specifically, SEM inserts an encoder before the input layer of the target model to map each cluster of synonyms to a unique encoding and trains the model to eliminate possible adversarial perturbations without modifying the network architecture or adding extra data. Extensive experiments demonstrate that SEM can effectively defend the current synonym substitution based attacks and block the transferability of adversarial examples. SEM is also easy and efficient to scale to large models and big datasets.

Natural Language Adversarial Defense through Synonym Encoding

In this paper, we investigate the non-stationary combinatorial semi-bandit problem, both in the switching case and in the dynamic case. In the general case where (a) the reward function is non-linear, (b) arms may be probabilistically triggered, and (c) only approximate offline oracle exists \cite{wang2017improving}, our algorithm achieves $\tilde{O}(\sqrt{N T})$ distribution-dependent regret in the switching case, and $\tilde{O}({V}^{1/3}T^{2/3})$ in the dynamic case, where ${N}$ is the number of switchings and ${V}$ is the sum of the total ``distribution changes''. The regret bounds in both scenarios are nearly optimal, but our algorithm needs to know the parameter ${N}$ or ${V}$ in advance.

Combinatorial Semi-Bandit in the Non-Stationary Environment

In a variety of problems, a decision-maker is unaware of the loss function associated with a task, yet it has to minimize this unknown loss in order to accomplish the task. Furthermore, the decision-maker's task may evolve, resulting in a varying loss function. In this setting, we explore sequential decision-making problems modeled by adversarial Markov decision processes, where the loss function may arbitrarily change at every time step. We consider the bandit feedback scenario, where the agent observes only the loss corresponding to its actions. We propose an algorithm, called online relative-entropy policy search with implicit exploration, that achieves a sublinear regret not only in expectation but, more importantly, with high probability. In particular, we prove that by employing an optimistically biased loss estimator, the proposed algorithm achieves a regret of $\tilde{\mathcal{O}}(T^{2/3} \sqrt{\tau|A||S|})$, where $|S|$ is the number of states, $|A|$ is the number of actions, $\tau$ is the mixing time, and $T$ is the time horizon. To our knowledge, the proposed algorithm is the first scheme that enjoys such high-probability regret bounds for general adversarial Markov decision processes under the presence of bandit feedback.

No-Regret Learning with High-Probability in Adversarial Markov Decision Processes

Graph neural networks (GNNs) are able to achieve promising performance on multiple graph downstream tasks such as node classification and link prediction. Comparatively lesser work has been done to design GNNs which can operate directly for community detection on graphs. Traditionally, GNNs are trained on a semi-supervised or self-supervised loss function and then clustering algorithms are applied to detect communities. However, such decoupled approaches are inherently sub-optimal. Designing an unsupervised loss function to train a GNN and extract communities in an integrated manner is a fundamental challenge. To tackle this problem, we combine the principle of self-expressiveness with the framework of self-supervised graph neural network for unsupervised community detection for the first time in literature. Our solution is trained in an end-to-end fashion and achieves state-of-the-art community detection performance on multiple publicly available datasets.

Unsupervised Constrained Community Detection via Self-Expressive Graph Neural Network

We study the problem of identifying the best arm in a stochastic multi-armed bandit game. Given a set of $n$ arms indexed from $1$ to $n$, each arm $i$ is associated with an unknown reward distribution supported on $[0,1]$ with mean $\theta_i$ and variance $\sigma_i^2$. Assume $\theta_1 > \theta_2 \geq \cdots \geq\theta_n$. We propose an adaptive algorithm which explores the gaps and variances of the rewards of the arms and makes future decisions based on the gathered information using a novel approach called \textit{grouped median elimination}. The proposed algorithm guarantees to output the best arm with probability $(1-\delta)$ and uses at most $O \left(\sum_{i = 1}^n \left(\frac{\sigma_i^2}{\Delta_i^2} + \frac{1}{\Delta_i}\right)(\ln \delta^{-1} + \ln \ln \Delta_i^{-1})\right)$ samples, where $\Delta_i$ ($i \geq 2$) denotes the reward gap between arm $i$ and the best arm and we define $\Delta_1 = \Delta_2$. This achieves a significant advantage over the variance-independent algorithms in some favorable scenarios and is the first result that removes the extra $\ln n$ factor on the best arm compared with the state-of-the-art. We further show that $\Omega \left( \sum_{i = 1}^n \left( \frac{\sigma_i^2}{\Delta_i^2} + \frac{1}{\Delta_i} \right) \ln \delta^{-1} \right)$ samples are necessary for an algorithm to achieve the same goal, thereby illustrating that our algorithm is optimal up to doubly logarithmic terms.

Variance-Dependent Best Arm Identification

We provide a general theoretical framework for stochastic continuous normalizing flows, an extension of continuous normalizing flows for density estimation of stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated. Doing so enables the treatment of SDEs as random ordinary differential equations, which can be trained using existing techniques. For scalar loss functions, this approach naturally recovers the stochastic adjoint method of Li et al. [2020] for training neural SDEs, while supporting a more flexible class of approximations.

Stochastic Continuous Normalizing Flows: Training SDEs as ODEs

This paper studies the probability distributions of penultimate activations of classification networks. Specifically, we show that, when a classification network is trained with the cross-entropy loss, its final classification layer forms a Generative-Discriminative pair with a generative classifier based on a specific distribution of penultimate activations. More importantly, the distribution is parameterized by the weights of the final fully-connected layer, and can be considered as a generative model that synthesizes the penultimate activations without feeding input data. We empirically demonstrate that this generative model enables stable knowledge distillation in the presence of domain shift, and can also transfer knowledge from a classifier to variational autoencoders and generative adversarial networks for class-conditional image generation.

On The Distribution of Penultimate Activations of Classification Networks

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain. Under certain conditions on the target distribution, we prove that $\tilde O(d^4\epsilon^{-2})$ stochastic gradient evaluations suffice to guarantee $\epsilon$-sampling error in terms of the total variation distance, where $d$ is the problem dimension. This improves existing results on the convergence rate of SGLD \citep{raginsky2017non,xu2018global}.

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Probabilistic task modelling for meta-learning

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