Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final value of those samples that are estimated more than once needs to be decided in some way. Averaging, the simplest approach, tends to produce blurred results. Significant work has been devoted to this issue in recent years: several works explore the idea of a weighted average of the overlapped patches and/or pixels; a more recent approach is to promote agreement (consensus) between the patches at their intersections. This work investigates the case where consensus is imposed as a hard constraint on the restoration problem. This leads to a general framework applicable to all sorts of signals, problems, decomposition strategies, and featuring a number of theoretical and practical advantages over other similar methods. The framework itself consists of a general optimization problem and a simple and efficient \admm-based algorithm for solving it. We also show that the consensus step of the algorithm, which is the main bottleneck of similar methods, can be solved efficiently and easily for any arbitrary patch decomposition scheme. As an example of the potential of our framework, we propose a method for filling missing samples (inpainting) which can be applied to signals of any dimension, and show its effectiveness on audio, image and video signals.

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving complex tasks, typically in an unsupervised or weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic-gradient-based neural network optimization. We illustrate the power of DRNets on de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku) and on a substantially more complex task in scientific discovery that concerns inferring crystal structures of materials from X-ray diffraction data under thermodynamic rules (Crystal-Structure-Phase-Mapping). At a high level, DRNets encode a structured latent space of the input data, which is constrained to adhere to prior knowledge by a reasoning module. The structured latent encoding is used by a generative decoder to generate the targeted output. Finally, an overall objective combines responses from the generative decoder (thinking fast) and the reasoning module (thinking slow), which is optimized using constraint-aware stochastic gradient descent. We show how to encode different tasks as DRNets and demonstrate DRNets' effectiveness with detailed experiments: DRNets significantly outperform the state of the art and experts' capabilities on Crystal-Structure-Phase-Mapping, recovering more precise and physically meaningful crystal structures. On Multi-MNIST-Sudoku, DRNets perfectly recovered the mixed Sudokus' digits, with 100% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. Finally, as a proof of concept, we also show how DRNets can solve standard combinatorial problems -- 9-by-9 Sudoku puzzles and Boolean satisfiability problems (SAT), outperforming other specialized deep learning models. DRNets are general and can be adapted and expanded to tackle other tasks.

Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical foundation lies on generalizations of Niemela's characterization of answer sets of a logic program via so called level rankings.

Mining temporal assertions from time-series data using information theory to filter real properties from incidental ones is a practically significant challenge. The problem is complex for continuous or hybrid systems because the degrees of influence on a consequent from a timed-sequence of predicates (called its prefix sequence), varies continuously over dense time intervals. We propose a parameterized method that uses interval arithmetic for flexibly learning prefix sequences having influence on a defined consequent over various time scales and predicates over system variables.

Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are both homogeneous and spatially contiguous. Second, it is well-recognized that landscapes are hierarchical such that fine-scale regions are nested wholly within broader-scale regions. To address these two challenges, first, we develop a spatially constrained spectral clustering framework for region delineation that incorporates the tradeoff between region homogeneity and spatial contiguity. The framework uses a flexible, truncated exponential kernel to represent the spatial contiguity constraints, which is integrated with the landscape feature similarity matrix for region delineation. To address the second challenge, we extend the framework to create fine-scale regions that are nested within broader-scaled regions using a greedy, recursive bisection approach. We present a case study of a terrestrial ecology data set in the United States that compares the proposed framework with several baseline methods for regionalization. Experimental results suggest that the proposed framework for regionalization outperforms the baseline methods, especially in terms of balancing region contiguity and homogeneity, as well as creating regions of more similar size, which is often a desired trait of regions.

A Knowledge Graph (KG), popularly used in both industry and academia, is an effective representation of knowledge. It consists of a collection of knowledge elements, each of which in turn is extracted from the web or other sources. Information extractors that use natural language processing techniques or other complex algorithms are usually noisy. That is, the vast number of knowledge elements extracted from the web may not only be associated with different confidence values but may also be inconsistent with each other. Many applications such as question answering systems that are built on top of large-scale KGs are required to reason efficiently about these confidence values and inconsistencies. In addition, they are required to incorporate ontological constraints in their reasoning. One way to do this is to extract a subgraph of a KG that is consistent with the ontological constraints and is of maximum total confidence value. Such a subgraph is referred to as the top hypothesis and is combinatorially hard to find. In this paper, we introduce an algorithmic framework for efficiently addressing the combinatorial hardness and selecting the top K hypotheses. Our approach is based on powerful algorithmic techniques recently invented in the context of the Weighted Constraint Satisfaction Problem (WCSP).

In this work, we present a novel human-in-the-loop framework to help the agent understand the decision making process that involves choosing preferred options. We focus on qualitative preference models over alternatives from combinatorial domains. This framework is interactive: e.g., the agent provides her behavioral data to the framework, and the framework ex- plains the learned model to the agent. It is iterative: the framework collects feedback on the learned model from the agent and tries to improve it accordingly until the agent terminates the iteration. In order to communicate the learned preference model to the agent, we focus on visualizing some of the intuitive and explain- able graphic models, such as lexicographic preference trees and forests, and conditional preference networks. To this end, we discuss key aspects of our framework, and demonstrate our prototype ready for lexicographic preference models.

Despite a tremendous amount of work in the literature and in the commercial sectors, current approaches to multi-modal trip planning still fail to consistently generate plans that users deem optimal in practice. We believe that this is due to the fact that current planners fail to capture the true preferences of users, e.g., their preferences depend on aspects that are not modeled. An example of this could be a preference not to walk through an unsafe area at night. We present a novel multi-modal trip planner that allows users to up- load auxiliary geographic data (e.g., crime rates) and to specify temporal constraints and preferences over these data in combination with typical metrics such as time and cost. Concretely, our planner supports the modes walking, biking, driving, public transit, and taxi, uses linear temporal logic to capture temporal constraints, and preferential cost functions to represent preferences. We show by examples that this allows the expression of very interesting preferences and constraints that, naturally, lead to quite diverse optimal plans.

In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector $v$. Then, we use $v$ to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1\% in the worst case.

Automated Planning is one of the main research field of Artificial Intelligence since its beginnings. Research in Automated Planning aims at developing general reasoners (i.e., planners) capable of automatically solve complex problems. Broadly speaking, planners rely on a general model characterizing the possible states of the world and the actions that can be performed in order to change the status of the world. Given a model and an initial known state, the objective of a planner is to synthesize a set of actions needed to achieve a particular goal state. The classical approach to planning roughly corresponds to the description given above. The timeline-based approach is a particular planning paradigm capable of integrating causal and temporal reasoning within a unified solving process. This approach has been successfully applied in many real-world scenarios although a common interpretation of the related planning concepts is missing. Indeed, there are significant differences among the existing frameworks that apply this technique. Each framework relies on its own interpretation of timeline-based planning and therefore it is not easy to compare these systems. Thus, the objective of this work is to investigate the timeline-based approach to planning by addressing several aspects ranging from the semantics of the related planning concepts to the modeling and solving techniques. Specifically, the main contributions of this PhD work consist of: (i) the proposal of a formal characterization of the timeline-based approach capable of dealing with temporal uncertainty; (ii) the proposal of a hierarchical modeling and solving approach; (iii) the development of a general purpose framework for planning and execution with timelines; (iv) the validation{\dag}of this approach in real-world manufacturing scenarios.