Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the generator of GANs have been reported. This paper will first theoretically analyze GANs' approximation property. Similar to the universal approximation property of the full connected neural networks with one hidden layer, we prove that the generator with the input latent variable in GANs can universally approximate the potential data distribution given the increasing hidden neurons. Furthermore, we propose an approach named stochastic data generation (SDG) to enhance GANs' approximation ability. Our approach is based on the simple idea of imposing randomness through data generation in GANs by a prior distribution on the conditional probability between the layers. Our approach can be easily implemented by using the reparameterization trick. The experimental results on synthetic dataset verify the improved approximation ability obtained by this SDG approach. In the practical dataset, the NSGAN/WGANGP with SDG can also outperform traditional GANs with little change in the model architectures.

This paper presents a framework for exemplar based generative modeling, featuring Exemplar VAEs. To generate a sample from the Exemplar VAE, one first draws a random exemplar from a training dataset, and then stochastically transforms that exemplar into a latent code, which is then used to generate a new observation. We show that the Exemplar VAE can be interpreted as a VAE with a mixture of Gaussians prior in the latent space, with Gaussian means defined by the latent encoding of the exemplars. To enable optimization and avoid overfitting, Exemplar VAE's parameters are learned using leave-one-out and exemplar subsampling, where, for the generation of each data point, we build a prior based on a random subset of the remaining data points. To accelerate learning, which requires finding the exemplars that exert the greatest influence on the generation of each data point, we use approximate nearest neighbor search in the latent space, yielding a lower bound on the log marginal likelihood. Experiments demonstrate the effectiveness of Exemplar VAEs in density estimation, representation learning, and generative data augmentation for supervised learning.

Speaker embeddings (x-vectors) extracted from very short segments of speech have recently been shown to give competitive performance in speaker diarization. We generalize this recipe by extracting from each speech segment, in parallel with the x-vector, also a diagonal precision matrix, thus providing a path for the propagation of information about the quality of the speech segment into a PLDA scoring backend. These precisions quantify the uncertainty about what the values of the embeddings might have been if they had been extracted from high quality speech segments. The proposed probabilistic embeddings (x-vectors with precisions) are interfaced with the PLDA model by treating the x-vectors as hidden variables and marginalizing them out. We apply the proposed probabilistic embeddings as input to an agglomerative hierarchical clustering (AHC) algorithm to do diarization in the DIHARD'19 evaluation set. We compute the full PLDA likelihood 'by the book' for each clustering hypothesis that is considered by AHC. We do joint discriminative training of the PLDA parameters and of the probabilistic x-vector extractor. We demonstrate accuracy gains relative to a baseline AHC algorithm, applied to traditional xvectors (without uncertainty), and which uses averaging of binary log-likelihood-ratios, rather than by-the-book scoring.

Log-based predictive maintenance of computing centers is a main concern regarding the worldwide computing grid that supports the CERN (European Organization for Nuclear Research) physics experiments. A log, as event-oriented adhoc information, is quite often given as unstructured big data. Log data processing is a time-consuming computational task. The goal is to grab essential information from a continuously changeable grid environment to construct a classification model. Evolving granular classifiers are suited to learn from time-varying log streams and, therefore, perform online classification of the severity of anomalies. We formulated a 4-class online anomaly classification problem, and employed time windows between landmarks and two granular computing methods, namely, Fuzzy-set-Based evolving Modeling (FBeM) and evolving Granular Neural Network (eGNN), to model and monitor logging activity rate. The results of classification are of utmost importance for predictive maintenance because priority can be given to specific time intervals in which the classifier indicates the existence of high or medium severity anomalies.

Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation of neighborhood relationships, (ii) handling data on a non-linear manifold, (iii) the capability of predicting projections for new test data points, (iv) interpretability of the system, and (v) the ability to reject test points if required. For this, we use a first-order Takagi-Sugeno type model. We generate rule antecedents using clusters in the input data. In this context, we also propose a new variant of the Geodesic c-means clustering algorithm. We estimate the rule parameters by minimizing an error function that preserves the inter-point geodesic distances (distances over the manifold) as Euclidean distances on the projected space. We apply the proposed method on three synthetic and three real-world data sets and visually compare the results with four other standard data visualization methods. The obtained results show that the proposed method behaves desirably and performs better than or comparable to the methods compared with. The proposed method is found to be robust to the initial conditions. The predictability of the proposed method for test points is validated by experiments. We also assess the ability of our method to reject output points when it should. Then, we extend this concept to provide a general framework for learning an unsupervised fuzzy model for data projection with different objective functions. To the best of our knowledge, this is the first attempt to manifold learning using unsupervised fuzzy modeling.

This paper investigates asymptotic properties of a class of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the mean, such as the median-of-means estimator. It is well known by now that the excess risk of resulting estimators often converges to 0 at the optimal rates under much weaker assumptions than those required by their "classical" counterparts. However, much less is known about asymptotic properties of the estimators themselves, for instance, whether robust analogues of the maximum likelihood estimators are asymptotically efficient. We make a step towards answering these questions and show that for a wide class of parametric problems, minimizers of the appropriately defined robust proxy of the risk converge to the minimizers of the true risk at the same rate, and often have the same asymptotic variance, as the estimators obtained by minimizing the usual empirical risk. Moreover, our results show that robust algorithms based on the so-called "min-max" type procedures in many cases provably outperform, is the asymptotic sense, algorithms based on direct risk minimization.

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by "controlled" Markov noise. In particular, the faster and slower recursions have non-additive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic behavior of our framework by relating it to limiting differential inclusions in both time scales that are defined in terms of the ergodic occupation measures associated with the controlled Markov processes. Using a special case of our results, we present a solution to the off-policy convergence problem for temporal-difference learning with linear function approximation. We compile several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability (i.e. the probability of convergence to a specific attractor of the limiting o.d.e. given that the iterates are in its domain of attraction after a sufficiently large number of iterations (say) n_0) framework to such recursions. We use these results to prove almost sure convergence of the iterates to the specified attractor when the iterates satisfy an "asymptotic tightness" condition. This, in turn, is shown to be useful in analyzing the tracking ability of general "adaptive" algorithms. Finally, we obtain the first informative error bounds on function approximation for the policy evaluation algorithm proposed by Basu et al. when the aim is to find the risk-sensitive cost represented using exponential utility. We show that this happens due to the absence of difference term in the earlier bound which is always present in all our bounds when the state space is large.

Diagnosing problems in Internet-scale services remains particularly difficult and costly for both content providers and ISPs. Because the Internet is decentralized, the cause of such problems might lie anywhere between an end-user's device and the service datacenters. Further, the set of possible problems and causes is not known in advance, making it impossible in practice to train a classifier with all combinations of problems, causes and locations. In this paper, we explore how different machine learning techniques can be used for Internet-scale root cause analysis using measurements taken from end-user devices. We show how to build generic models that (i) are agnostic to the underlying network topology, (ii) do not require to define the full set of possible causes during training, and (iii) can be quickly adapted to diagnose new services. Our solution, DiagNet, adapts concepts from image processing research to handle network and system metrics. We evaluate DiagNet with a multi-cloud deployment of online services with injected faults and emulated clients with automated browsers. We demonstrate promising root cause analysis capabilities, with a recall of 73.9% including causes only being introduced at inference time.

'Capsule' models try to explicitly represent the poses of objects, enforcing a linear relationship between an object's pose and that of its constituent parts. This modelling assumption should lead to robustness to viewpoint changes since the sub-object/super-object relationships are invariant to the poses of the object. We describe a probabilistic generative model which encodes such capsule assumptions, clearly separating the generative parts of the model from the inference mechanisms. With a variational bound we explore the properties of the generative model independently of the approximate inference scheme, and gain insights into failures of the capsule assumptions and inference amortisation. We experimentally demonstrate the applicability of our unified objective, and demonstrate the use of test time optimisation to solve problems inherent to amortised inference in our model.

Recursive Bayesian inference (RBI) provides optimal Bayesian latent variable estimates in real-time settings with streaming noisy observations. Active RBI attempts to effectively select queries that lead to more informative observations to rapidly reduce uncertainty until a confident decision is made. However, typically the optimality objectives of inference and query mechanisms are not jointly selected. Furthermore, conventional active querying methods stagger due to misleading prior information. Motivated by information theoretic approaches, we propose an active RBI framework with unified inference and query selection steps through Renyi entropy and $\alpha$-divergence. We also propose a new objective based on Renyi entropy and its changes called Momentum that encourages exploration for misleading prior cases. The proposed active RBI framework is applied to the trajectory of the posterior changes in the probability simplex that provides a coordinated active querying and decision making with specified confidence. Under certain assumptions, we analytically demonstrate that the proposed approach outperforms conventional methods such as mutual information by allowing the selections of unlikely events. We present empirical and experimental performance evaluations on two applications: restaurant recommendation and brain-computer interface (BCI) typing systems.