We propose injective generative models called Trumpets that generalize invertible normalizing flows. The proposed generators progressively increase dimension from a low-dimensional latent space. We demonstrate that Trumpets can be trained orders of magnitudes faster than standard flows while yielding samples of comparable or better quality. They retain many of the advantages of the standard flows such as training based on maximum likelihood and a fast, exact inverse of the generator. Since Trumpets are injective and have fast inverses, they can be effectively used for downstream Bayesian inference. To wit, we use Trumpet priors for maximum a posteriori estimation in the context of image reconstruction from compressive measurements, outperforming competitive baselines in terms of reconstruction quality and speed. We then propose an efficient method for posterior characterization and uncertainty quantification with Trumpets by taking advantage of the low-dimensional latent space.

Teddy Seidenfeld has been arguing for quite a long time that binary preference models are not powerful enough to deal with a number of crucial aspects of imprecision and indeterminacy in uncertain inference and decision making. It is at his insistence that we initiated our study of so-called sets of desirable option sets, which we have argued elsewhere provides an elegant and powerful approach to dealing with general, binary as well as non-binary, decision-making under uncertainty. We use this approach here to explore an interesting notion of irrelevance (and independence), first suggested by Seidenfeld in an example intended as a criticism of a number of specific decision methodologies based on (convex) binary preferences. We show that the consequences of making such an irrelevance or independence assessment are very strong, and might be used to argue for the use of so-called mixing choice functions, and E-admissibility as the resulting decision scheme.

We present a new type of acquisition functions for online decision making in multi-armed and contextual bandit problems with extreme payoffs. Specifically, we model the payoff function as a Gaussian process and formulate a novel type of upper confidence bound (UCB) acquisition function that guides exploration towards the bandits that are deemed most relevant according to the variability of the observed rewards. This is achieved by computing a tractable likelihood ratio that quantifies the importance of the output relative to the inputs and essentially acts as an \textit{attention mechanism} that promotes exploration of extreme rewards. We demonstrate the benefits of the proposed methodology across several synthetic benchmarks, as well as a realistic example involving noisy sensor network data. Finally, we provide a JAX library for efficient bandit optimization using Gaussian processes.

Sentiment analysis is a vast area in the Machine learning domain. A lot of work is done on datasets and their analysis of the English Language. In Pakistan, a huge amount of data is in roman Urdu language, it is scattered all over the social sites including Twitter, YouTube, Facebook and similar applications. In this study the focus domain of dataset gathering is YouTube comments. The Dataset contains the comments of people over different Pakistani dramas and TV shows. The Dataset contains multi-class classification that is grouped The comments into positive, negative and neutral sentiment. In this Study comparative analysis is done for five supervised learning Algorithms including linear regression, SVM, KNN, Multi layer Perceptron and Na\"ive Bayes classifier. Accuracy, recall, precision and F-measure are used for measuring performance. Results show that accuracy of SVM is 64 percent, which is better than the rest of the list.

The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and white Gaussian noise. Due to its relative simplicity and general effectiveness, the Kalman filter is widely used in engineering applications. Since many sensory problems the brain faces are, at their core, filtering problems, it is possible that the brain possesses neural circuitry that implements equivalent computations to the Kalman filter. The standard approach to Kalman filtering requires complex matrix computations that are unlikely to be directly implementable in neural circuits. In this paper, we show that a gradient-descent approximation to the Kalman filter requires only local computations with variance weighted prediction errors. Moreover, we show that it is possible under the same scheme to adaptively learn the dynamics model with a learning rule that corresponds directly to Hebbian plasticity. We demonstrate the performance of our method on a simple Kalman filtering task, and propose a neural implementation of the required equations. The Bayesian Brain hypothesis has gained significant traction in cognitive neuroscience over the last two decades (Knill and Pouget, 2004; Doya et al., 2007; Pouget et al., 2013).

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs strictly subsume many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show huge potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

The Intergovernmental Panel on Climate Change (IPCC) fifth assessment report states that warming of the climate system is unequivocal and notes that each of the last three decades has been successively warmer at the Earth's surface than any preceding decade since 1850. The projections of the IPCC Report regarding future global temperature change range from 1.1 to 4 C, but that temperatures increases of more than 6 C cannot be ruled out [1]. This wide range of values reflects our limitations in performing accurate projections of future climate change produced by different potential pathways of greenhouse gas (GHG) emissions. The sources of the uncertainty that prevent us from obtaining better precision are diverse. One of them is related to the computer models used to project future climate change.

Deciding what's next? is a fundamental problem in robotics and Artificial Intelligence. Under belief space planning (BSP), in a partially observable setting, it involves calculating the expected accumulated belief-dependent reward, where the expectation is with respect to all future measurements. Since solving this general un-approximated problem quickly becomes intractable, state of the art approaches turn to approximations while still calculating planning sessions from scratch. In this work we propose a novel paradigm, Incremental BSP (iX-BSP), based on the key insight that calculations across planning sessions are similar in nature and can be appropriately re-used. We calculate the expectation incrementally by utilizing Multiple Importance Sampling techniques for selective re-sampling and re-use of measurement from previous planning sessions. The formulation of our approach considers general distributions and accounts for data association aspects. We demonstrate how iX-BSP could benefit existing approximations of the general problem, introducing iML-BSP, which re-uses calculations across planning sessions under the common Maximum Likelihood assumption. We evaluate both methods and demonstrate a substantial reduction in computation time while statistically preserving accuracy. The evaluation includes both simulation and real-world experiments considering autonomous vision-based navigation and SLAM. As a further contribution, we introduce to iX-BSP the non-integral wildfire approximation, allowing one to trade accuracy for computational performance by averting from updating re-used beliefs when they are "close enough". We evaluate iX-BSP under wildfire demonstrating a substantial reduction in computation time while controlling the accuracy sacrifice. We also provide analytical and empirical bounds of the effect wildfire holds over the objective value.

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and obtains a direct approximation of the posterior density. Compared to Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. In the simulation study conducted here, the proposed VB approach detects various types of proper active structures for dynamic network models. Compared to the alternative approach, the proposed method achieves similar or better accuracy, and its computational time is halved. In a real data analysis scenario of day-ahead natural gas flow prediction in the German gas transmission network with 51 nodes between October 2013 and September 2015, the VB approach delivers promising forecasting accuracy along with clearly detected structures in terms of dynamic dependence.

The importance of Variational Autoencoders reaches far beyond standalone generative models -- the approach is also used for learning latent representations and can be generalized to semi-supervised learning. This requires a thorough analysis of their commonly known shortcomings: posterior collapse and approximation errors. This paper analyzes VAE approximation errors caused by the combination of the ELBO objective with the choice of the encoder probability family, in particular under conditional independence assumptions. We identify the subclass of generative models consistent with the encoder family. We show that the ELBO optimizer is pulled from the likelihood optimizer towards this consistent subset. Furthermore, this subset can not be enlarged, and the respective error cannot be decreased, by only considering deeper encoder networks.