Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

The usage of deep generative models for image compression has led to impressive performance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling approach to compress temporal sequences with a focus on video. Our approach builds upon variational autoencoder (VAE) models for sequential data and combines them with recent work on neural image compression. The approach jointly learns to transform the original sequence into a lower-dimensional representation as well as to discretize and entropy code this representation according to predictions of the sequential VAE. Rate-distortion evaluations on small videos from public data sets with varying complexity and diversity show that our model yields competitive results when trained on generic video content. Extreme compression performance is achieved when training the model on specialized content.

Probability is a measure of uncertainty. Probability applies to machine learning because in the real world, we need to make decisions with incomplete information. Hence, we need a mechanism to quantify uncertainty – which Probability provides us. Using probability, we can model elements of uncertainty such as risk in financial transactions and many other business processes. In contrast, in traditional programming, we work with deterministic problems i.e. the solution is not affected by uncertainty.

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past posterior discoveries become future prior beliefs, to the infinite functional space setting of GP. For a reason of scalability, we introduce variational inference together with an sparse approximation based on inducing inputs. As a consequence, we obtain tractable continual lower-bounds where two novel Kullback-Leibler (KL) divergences intervene in a natural way. The key technical property of our method is the recursive reconstruction of conditional GP priors conditioned on the variational parameters learned so far. To achieve this goal, we introduce a novel factorization of past variational distributions, where the predictive GP equation propagates the posterior uncertainty forward. We then demonstrate that it is possible to derive GP models over many types of sequential observations, either discrete or continuous and amenable to stochastic optimization. The continual inference approach is also applicable to scenarios where potential multi-channel or heterogeneous observations might appear. Extensive experiments demonstrate that the method is fully scalable, shows a reliable performance and is robust to uncertainty error propagation over a plenty of synthetic and real-world datasets.

Learning exists in the context of data, yet notions of $\textit{confidence}$ typically focus on model predictions, not label quality. Confident learning (CL) has emerged as an approach for characterizing, identifying, and learning with noisy labels in datasets, based on the principles of pruning noisy data, counting to estimate noise, and ranking examples to train with confidence. Here, we generalize CL, building on the assumption of a classification noise process, to directly estimate the joint distribution between noisy (given) labels and uncorrupted (unknown) labels. This generalized CL, open-sourced as $\texttt{cleanlab}$, is provably consistent under reasonable conditions, and experimentally performant on ImageNet and CIFAR, outperforming recent approaches, e.g. MentorNet, by $30\%$ or more, when label noise is non-uniform. $\texttt{cleanlab}$ also quantifies ontological class overlap, and can increase model accuracy (e.g. ResNet) by providing clean data for training.

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a mismatch between the model and inference. Motivated by this, we consider the sampler-induced distribution as the model of interest and maximize the likelihood of this model. This yields a class of energy-inspired models (EIMs) that incorporate learned energy functions while still providing exact samples and tractable log-likelihood lower bounds. We describe and evaluate three instantiations of such models based on truncated rejection sampling, self-normalized importance sampling, and Hamiltonian importance sampling. These models outperform or perform comparably to the recently proposed Learned Accept/Reject Sampling algorithm and provide new insights on ranking Noise Contrastive Estimation and Contrastive Predictive Coding. Moreover, EIMs allow us to generalize a recent connection between multi-sample variational lower bounds and auxiliary variable variational inference. We show how recent variational bounds can be unified with EIMs as the variational family.

Black Box Machine Learning models leak information about the proprietary model parameters and architecture, both through side channels and output predictions. An adversary can thus, exploit this leakage to reconstruct a substitute architecture similar to the target model, violating the model privacy and Intellectual Property. However, all such attacks, infer a subset of the target model attributes and identifying the rest of the architecture and parameters (optimally) is a search problem. Extracting the exact target model is not possible owing to the uncertainty in the inference attack outputs and stochastic nature of the training process. In this work, we propose a probabilistic framework, Airavata, to estimate the leakage in such model extraction attacks. Specifically, we use Bayesian Networks to capture the uncertainty, under the subjective notion of probability, in estimating the target model attributes using various model extraction attacks. We experimentally validate the model under different adversary assumptions commonly adopted by various model extraction attacks to reason about the attack efficacy. Further, this provides a practical approach of inferring actionable knowledge about extracting black box models and identify the best combination of attacks which maximise the knowledge extracted (information leaked) from the target model.

W e argue the case for Gaussian Belief Propagation (GBP) as a strong algorithmic framework for the distributed, generic and incremental probabilistic estimation we need in Spatial AI as we aim at high performance smart robots and devices which operate within the constraints of real products. Processor hardware is changing rapidly, and GBP has the right character to take advantage of highly distributed processing and storage while estimating global quantities, as well as great flexibility. W e present a detailed tutorial on GBP, relating to the standard factor graph formulation used in robotics and computer vision, and give several simulation examples with code which demonstrate its properties.

Regularization methods, specifically those which directly alter weights like $L_1$ and $L_2$, are an integral part of many learning algorithms. Both the regularizers mentioned above are formulated by assuming certain priors in the parameter space and these assumptions, in some cases, induce sparsity in the parameter space. Regularizers help in transferring beliefs one has on the dataset or the parameter space by introducing adequate terms in the loss function. Any kind of formulation represents a specific set of beliefs: $L_1$ regularization conveys that the parameter space should be sparse whereas $L_2$ regularization conveys that the parameter space should be bounded and continuous. These regularizers in turn leverage certain priors to express these inherent beliefs. A better understanding of how the prior affects the behavior of the parameters and how the priors can be updated based on the dataset can contribute greatly in improving the generalization capabilities of a function estimator. In this work, we introduce a weakly informative prior and then further extend it to an informative prior in order to formulate a regularization penalty, which shows better results in terms of inducing sparsity experimentally, when compared to regularizers based only on Gaussian and Laplacian priors. Experimentally, we verify that a regularizer based on an adapted prior improves the generalization capabilities of any network. We illustrate the performance of the proposed method on the MNIST and CIFAR-10 datasets.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to form "exact approximations" to otherwise intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs and particle Gibbs with ancestor sampling, improving their performance beyond that of the underlying Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter prior is conjugate to the complete data likelihood. Marginalization yields a non-Markovian model for inference, but we show that, in contrast to the general case, this method still scales linearly in time. While marginalization can be cumbersome to implement, recent advances in probabilistic programming have enabled its automation. We demonstrate how the marginalized methods are viable as efficient inference backends in probabilistic programming, and demonstrate with examples in ecology and epidemiology.