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.

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.

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.

Unsupervised learning seeks to uncover patterns in data. However, different kinds of noise may impede the discovery of useful substructure from real-world time-series data. In this work, we focus on mitigating the interference of left-censorship in the task of clustering. We provide conditions under which clusters and left-censorship may be identified; motivated by this result, we develop a deep generative, continuous-time model of time-series data that clusters while correcting for censorship time. We demonstrate accurate, stable, and interpretable results on synthetic data that outperform several benchmarks. To showcase the utility of our framework on real-world problems, we study how left-censorship can adversely affect the task of disease phenotyping, resulting in the often incorrect assumption that longitudinal patient data are aligned by disease stage. In reality, patients at the time of diagnosis are at different stages of the disease -- both late and early due to differences in when patients seek medical care and such discrepancy can confound unsupervised learning algorithms. On two clinical datasets, our model corrects for this form of censorship and recovers known clinical subtypes.

Learning probability measures based on an i.i.d. sample is a fundamental inference task, but is challenging when the sample space is high-dimensional. Inspired by the success of tree boosting in high-dimensional classification and regression, we propose a tree boosting method for learning high-dimensional probability distributions. We formulate concepts of "addition'' and "residuals'' on probability distributions in terms of compositions of a new, more general notion of multivariate cumulative distribution functions (CDFs) than classical CDFs. This then gives rise to a simple boosting algorithm based on forward-stagewise (FS) fitting of an additive ensemble of measures. The output of the FS algorithm allows analytic computation of the probability density function for the fitted distribution. It also provides an exact simulator for drawing independent Monte Carlo samples from the fitted measure. Typical considerations in applying boosting -- namely choosing the number of trees, setting the appropriate level of shrinkage/regularization in the weak learner, and the evaluation of variable importance -- can be accomplished in an analogous fashion to traditional boosting in supervised learning. Numerical experiments confirm that boosting can substantially improve the fit to multivariate distributions compared to the state-of-the-art single-tree learner and is computationally efficient. We illustrate through an application to a data set from mass cytometry how the simulator can be used to investigate various aspects of the underlying distribution.

Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their information-processing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the Kullblack-Leibler divergence between posterior decisions and prior beliefs. When information acquisition is free, the \textit{homo economicus} agent is recovered, while in cases when information acquisition becomes costly, agents instead revert to their prior beliefs. The maximum entropy principle is used to infer least-biased decisions, based upon the notion of Smithian competition formalised within the Quantal Response Statistical Equilibrium framework. The incorporation of prior beliefs into such a framework allowed us to systematically explore the effects of prior beliefs on decision-making, in the presence of market feedback. We verified the proposed model using Australian housing market data, showing how the incorporation of prior knowledge alters the resulting agent decisions. Specifically, it allowed for the separation (and analysis) of past beliefs and utility maximisation behaviour of the agent.

In this work, we propose a Bayesian statistical model to simultaneously characterize two or more social networks defined over a common set of actors. The key feature of the model is a hierarchical prior distribution that allows us to represent the entire system jointly, achieving a compromise between dependent and independent networks. Among others things, such a specification easily allows us to visualize multilayer network data in a low-dimensional Euclidean space, generate a weighted network that reflects the consensus affinity between actors, establish a measure of correlation between networks, assess cognitive judgements that subjects form about the relationships among actors, and perform clustering tasks at different social instances. Our model's capabilities are illustrated using several real-world data sets, taking into account different types of actors, sizes, and relations.

Bayesian optimization (BO) is among the most effective and widely-used blackbox optimization methods. BO proposes solutions according to an explore-exploit trade-off criterion encoded in an acquisition function, many of which are computed from the posterior predictive of a probabilistic surrogate model. Prevalent among these is the expected improvement (EI) function. The need to ensure analytical tractability of the predictive often poses limitations that can hinder the efficiency and applicability of BO. In this paper, we cast the computation of EI as a binary classification problem, building on the link between class-probability estimation and density-ratio estimation, and the lesser-known link between density-ratios and EI. By circumventing the tractability constraints, this reformulation provides numerous advantages, not least in terms of expressiveness, versatility, and scalability.