This paper studies active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework.  We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

Exponential Random Graphs Models (ERGM) are common, simple statistical models for social network and other network structures. Unfortunately, inference and learning with them is hard even for small networks because their partition functions are intractable for precise computation. In this paper, we introduce a new quadratic time deterministic approximation to these partition functions. Our main insight enabling this advance is that subgraph statistics is sufficient to derive a lower bound for partition functions given that the model is not dominated by a few graphs. The proposed method differs from existing methods in its ways of exploiting asymptotic properties of subgraph statistics. Compared to the current Monte Carlo simulation based methods, the new method is scalable, stable, and precise enough for inference tasks.

Modeling real world domains requires ever more frequently to represent uncertain information. The DISPONTE semantics for probabilistic description logics allows to annotate axioms of a knowledge base with a value that represents their probability. In this paper we discuss approaches for performing inference from probabilistic ontologies following the DISPONTE semantics. We present the algorithm BUNDLE for computing the probability of queries. BUNDLE exploits an underlying Description Logic reasoner, such as Pellet, in order to find explanations for a query. These are then encoded in a Binary Decision Diagram that is used for computing the probability of the query.

Most multi-label domains lack an authoritative taxonomy. Therefore, different taxonomies are commonly used in the same domain, which results in complications. Although this situation occurs frequently, there has been little study of it using a principled statistical approach. Given that (1) different taxonomies used in the same domain are generally founded on the same latent semantic space, where each possible label set in a taxonomy denotes a single semantic concept, and that (2) crowdsourcing is beneficial in identifying relationships between semantic concepts and instances at low cost, we proposed a novel probabilistic cascaded method for establishing a semantic matching function in a crowdsourcing setting that maps label sets in one (source) taxonomy to label sets in another (target) taxonomy in terms of the semantic distances between them. The established function can be used to detect the associated label set in the target taxonomy for an instance directly from its associated label set in the source taxonomy without any extra effort. Experimental results on real-world data (emotion annotations for narrative sentences) demonstrated that the proposed method can robustly establish semantic matching functions exhibiting satisfactory performance from a limited number of crowdsourced annotations.

This paper revisits the problem of learning a k-CNF Boolean function from examples, for fixed k, in the context of online learning under the logarithmic loss. We give a Bayesian interpretation to one of Valiant’s classic PAC learning algorithms, which we then build upon to derive three efficient, online, probabilistic, supervised learning algorithms for predicting the output of an unknown k-CNF Boolean function. We analyze the loss of our methods, and show that the cumulative log-loss can be upper bounded by a polynomial function of the size of each example.

This thesis focuses on the problem of temporal planning under uncertainty with explicit safety guarantees, which are enforced by means of chance constraints. We aim at elevating the level in which operators interact with autonomous agents and specify their desired behavior, while retaining a keen sensitivity to risk. Instead of relying on unconditional sequences, our goal is to allow contingent plans to be dynamically scheduled and conditioned on observations of the world while remaining safe. Contingencies add flexibility by allowing goals to be achieved through different methods, while observations allow the agent to adapt to the environment. We demonstrate the usefulness of our chance-constrained temporal planning approaches in real-world applications, such as partially observable power supply restoration and collaborative human-robot manufacturing.

Graphical models, such as Bayesian Networks and Markov networks play an important role in artificial intelligence and machine learning. Inference is a central problem to be solved on these networks. This, and other problems on these graph models are often known to be hard to solve in general, but tractable on graphs with bounded Treewidth. Therefore, finding or approximating the Treewidth of a graph is a fundamental problem related to inference in graphical models. In this paper, we study the approximability of a number of graph problems: Treewidth and Pathwidth of graphs, Minimum Fill-In, and a variety of different graph layout problems such as Minimum Cut Linear Arrangement. We show that, assuming Small Set Expansion Conjecture, all of these problems are NP-hard to approx- imate to within any constant factor in polynomial time.

Markov chain Monte Carlo (MCMC) is a popular tool for Bayesian inference.However, MCMC cannot be practically applied to large data sets because of theprohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) MCMC algorithm with auxiliary variables that only queries the likelihoods of a subset of the data at each iteration yet simulates from the exact posterior distribution. FlyMC is compatible with modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors. In experiments, we find that FlyMC generates samples from the posterior more than an order of magnitude faster than regular MCMC, allowing MCMC methods to tackle larger datasets than were previously considered feasible.

In this paper, we study Bayesian techniques for entity discovery and temporal segmentation of videos. Existing temporal video segmentation techniques are based on low-level features, and are usually suitable for discovering short, homogeneous shots rather than diverse scenes, each of which contains several such shots. We define scenes in terms of semantic entities (eg. persons). This is the first attempt at entity-driven scene discovery in videos, without using meta-data like scripts. The problem is hard because we have no explicit prior information about the entities and the scenes. However such sequential data exhibit temporal coherence in multiple ways, and this provides implicit cues. To capture these, we propose a Bayesian generative model- EntScene, that represents entities with mixture components and scenes with discrete distributions over these components. The most challenging part of this approach is the inference, as it involves complex interactions of latent variables. To this end, we propose an algorithm based on Dynamic Blocked Gibbs Sampling, that attempts to jointly learn the components and the segmentation, by progressively merging an initial set of short segments. The proposed algorithm compares favourably against suitably designed baselines on several TV-series videos. We extend the method to an unexplored problem: temporal co-segmentation of videos containing same entities.

We propose a technique for decomposing and compressing the dataset in the parameter learning problem in Markov random fields. Our technique applies to incomplete datasets and exploits variables that are always observed in the given dataset. We show that our technique allows exact computation of the gradient and the likelihood, and can lead to orders-of-magnitude savings in learning time.