Communication changes the beliefs of the listener and of the speaker. The value of a communicative act stems from the valuable belief states which result from this act. To model this we build on the Interactive POMDP (IPOMDP) framework, which extends POMDPs to allow agents to model others in multi-agent settings, and we include communication that can take place between the agents to formulate Communicative IPOMDPs (CIPOMDPs). We treat communication as a type of action and therefore, decisions regarding communicative acts are based on decision-theoretic planning using the Bellman optimality principle and value iteration, just as they are for all other rational actions. As in any form of planning, the results of actions need to be precisely specified. We use the Bayes' theorem to derive how agents update their beliefs in CIPOMDPs; updates are due to agents' actions, observations, messages they send to other agents, and messages they receive from others. The Bayesian decision-theoretic approach frees us from the commonly made assumption of cooperative discourse - we consider agents which are free to be dishonest while communicating and are guided only by their selfish rationality. We use a simple Tiger game to illustrate the belief update, and to show that the ability to rationally communicate allows agents to improve efficiency of their interactions.

Recently I came across an interesting Paper named, "Deep Ensembles: A Loss Landscape Perspective" by a Laxshminarayan et al.In this article, I will break down the paper, summarise it's findings and delve into some of the techniques and strategies they used that will be useful for delving into understanding models and their learning process. It will also go over some possible extensions to the paper. You can also find my annotations on the paper down below. The authors conjectured (correctly) that Deep Ensembles (an ensemble of Deep learning models) outperform Bayesian Neural Networks because "popular scalable variational Bayesian methods tend to focus on a single mode, whereas deep ensembles tend to explore diverse modes in function space." In simple words, when running a Bayesian Network at a single initialization it will reach one of the peaks and stop.

Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of how past events might affect an event's present probability, we propose using a temporal deductive database to track structured facts over time. Rules serve to prove facts from other facts and from past events. Each fact has a time-varying state---a vector computed by a neural net whose topology is determined by the fact's provenance, including its experience of past events. The possible event types at any time are given by special facts, whose probabilities are neurally modeled alongside their states. In both synthetic and real-world domains, we show that neural probabilistic models derived from concise Datalog programs improve prediction by encoding appropriate domain knowledge in their architecture.

Despite deep neural network (DNN)'s impressive prediction performance in various domains, it is well known now that a set of DNN models trained with the same model specification and the same data can produce very different prediction results. Ensemble method is one state-of-the-art benchmark for prediction uncertainty estimation. However, ensembles are expensive to train and serve for web-scale traffic. In this paper, we seek to advance the understanding of prediction variation estimated by the ensemble method. Through empirical experiments on two widely used benchmark datasets MovieLens and Criteo in recommender systems, we observe that prediction variations come from various randomness sources, including training data shuffling, and parameter random initialization. By introducing more randomness into model training, we notice that ensemble's mean predictions tend to be more accurate while the prediction variations tend to be higher. Moreover, we propose to infer prediction variation from neuron activation strength and demonstrate the strong prediction power from activation strength features. Our experiment results show that the average R squared on MovieLens is as high as 0.56 and on Criteo is 0.81. Our method performs especially well when detecting the lowest and highest variation buckets, with 0.92 AUC and 0.89 AUC respectively. Our approach provides a simple way for prediction variation estimation, which opens up new opportunities for future work in many interesting areas (e.g.,model-based reinforcement learning) without relying on serving expensive ensemble models.

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic, design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models.

Due to data protection laws sensitive personal data cannot be released or shared among businesses as well as scientific institutions. While anonymization techniques are becoming increasingly popular, they often raise security concerns and have been re-identified in some cases Narayanan and Shmatikov (2010). To be on the safe side, big data collecting organisation such as Eurostat (statistical office of the European Union) or the World Bank only release aggregated summaries of their data. E.g.: Instead of individual salary data only selected quantiles of the population distribution are available. Thus, for exploratory analysis as well as statistical modeling, the need for methods which work on aggregated data is there.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem.

The projected belief network (PBN) is a layered generative network with tractable likelihood function, and is based on a feed-forward neural network (FF-NN). It can therefore share an embodiment with a discriminative classifier and can inherit the best qualities of both types of network. In this paper, a convolutional PBN is constructed that is both fully discriminative and fully generative and is tested on spectrograms of spoken commands. It is shown that the network displays excellent qualities from either the discriminative or generative viewpoint. Random data synthesis and visible data reconstruction from low-dimensional hidden variables are shown, while classifier performance approaches that of a regularized discriminative network. Combination with a conventional discriminative CNN is also demonstrated.

We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty information is useful, for example, for an adaptive testing scenario, where additional tests can be administered if the model is not quite certain about a students' skill level estimation. Traditional Bayesian inference methods that produce such uncertainty information are computationally expensive and do not scale to large data sets. VarFA utilizes variational inference which makes it possible to efficiently perform Bayesian inference even on very large data sets. We use the sparse factor analysis model as a case study and demonstrate the efficacy of VarFA on both synthetic and real data sets. VarFA is also very general and can be applied to a wide array of factor analysis models.

We investigate optimal posteriors for recently introduced \cite{begin2016pac} chi-squared divergence based PAC-Bayesian bounds in terms of nature of their distribution, scalability of computations, and test set performance. For a finite classifier set, we deduce bounds for three distance functions: KL-divergence, linear and squared distances. Optimal posterior weights are proportional to deviations of empirical risks, usually with subset support. For uniform prior, it is sufficient to search among posteriors on classifier subsets ordered by these risks. We show the bound minimization for linear distance as a convex program and obtain a closed-form expression for its optimal posterior. Whereas that for squared distance is a quasi-convex program under a specific condition, and the one for KL-divergence is non-convex optimization (a difference of convex functions). To compute such optimal posteriors, we derive fast converging fixed point (FP) equations. We apply these approaches to a finite set of SVM regularization parameter values to yield stochastic SVMs with tight bounds. We perform a comprehensive performance comparison between our optimal posteriors and known KL-divergence based posteriors on a variety of UCI datasets with varying ranges and variances in risk values, etc. Chi-squared divergence based posteriors have weaker bounds and worse test errors, hinting at an underlying regularization by KL-divergence based posteriors. Our study highlights the impact of divergence function on the performance of PAC-Bayesian classifiers. We compare our stochastic classifiers with cross-validation based deterministic classifier. The latter has better test errors, but ours is more sample robust, has quantifiable generalization guarantees, and is computationally much faster.