This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing pattern mining with background knowledge, which has been a data mining issue for a long time. We propose encodings of the classical sequential pattern mining tasks within two representations of embeddings (fill-gaps vs skip-gaps) and for various kinds of patterns: frequent, constrained and condensed. We compare the computational performance of these encodings with each other to get a good insight into the efficiency of ASP encodings. The results show that the fill-gaps strategy is better on real problems due to lower memory consumption. Finally, compared to a constraint programming approach (CPSM), another declarative programming paradigm, our proposal showed comparable performance.

We used redescription mining to find interpretable rules revealing associations between those determinants that provide insights about the Alzheimer's disease (AD). We extended the CLUS-RM redescription mining algorithm to a constraint-based redescription mining (CBRM) setting, which enables several modes of targeted exploration of specific, user-constrained associations. Redescription mining enabled finding specific constructs of clinical and biological attributes that describe many groups of subjects of different size, homogeneity and levels of cognitive impairment. We confirmed some previously known findings. However, in some instances, as with the attributes: testosterone, the imaging attribute Spatial Pattern of Abnormalities for Recognition of Early AD, as well as the levels of leptin and angiopoietin-2 in plasma, we corroborated previously debatable findings or provided additional information about these variables and their association with AD pathogenesis. Applying redescription mining on ADNI data resulted with the discovery of one largely unknown attribute: the Pregnancy-Associated Protein-A (PAPP-A), which we found highly associated with cognitive impairment in AD. Statistically significant correlations (p <= 0.01) were found between PAPP-A and various different clinical tests. The high importance of this finding lies in the fact that PAPP-A is a metalloproteinase, known to cleave insulin-like growth factor binding proteins. Since it also shares similar substrates with A Disintegrin and the Metalloproteinase family of enzymes that act as {\alpha}-secretase to physiologically cleave amyloid precursor protein (APP) in the non-amyloidogenic pathway, it could be directly involved in the metabolism of APP very early during the disease course. Therefore, further studies should investigate the role of PAPP-A in the development of AD more thoroughly.

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a, b)-supermatch is a stable matching in which if any a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and the partners of at most b other pairs. In this context, we define the most robust stable matching as a (1, b)- supermatch where b is minimum. We first show that checking whether a given stable matching is a (1, b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances shows that local search outperforms the other approaches.

Artificial Intelligence/Machine Learning field is getting a lot of attention right now, and knowing where to start can be a little difficult. I've been dabbling in this field, so I thought of curating the best resources in one place. All of these are curated based on if it's an inspiring read or a valuable resource. I hope this curated list help you get started on what you need to know about AI/Machine Learning on a technical level. Design intelligent agents to solve real-world problems including, search, games, machine learning, logic, and constraint satisfaction problems.

Recently, a number of noteworthy results have been achieved in various fields of artificial intelligence, and many aspects of the problem solving process have received significant attention by the scientific community. In this context, the extraction of comprehensive knowledge suitable for problem solving and reasoning, from textual and pictorial problem descriptions, has been less investigated, but recognized as essential for autonomous thinking in Artificial Intelligence. In this work we present a challenge where methods and tools for deep understanding are strongly needed for enabling problem solving: we propose to solve mathematical puzzles by means of computers, starting from text and diagrams describing them, without any human intervention. We are aware that the proposed challenge is hard and of difficult solution nowadays (and in the foreseeable future), but even studying and solving only single parts of the proposed challenge would represent an important step forward for artificial intelligence.

In this paper, we present Solus Forge, a system for designing and generating 3D Lego models from a decomposition of the model into pieces and a series of spatial constraints over those pieces. We also include a style specification, which provides a series of transformations to perform on the initial model; adding, removing or modifying various pieces. To generate the models, we use a two-stage constraint solving process in which we first solve for the layout of the final model before then solving for the specific layout of the individual Lego pieces. In this way, we provide a framework for models that incorporates a specific set of criteria but also can be modified to fit a designer's needs.

Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct problem for which one looks for a (non-necessarily contiguous) rectangular sub-matrix with a maximal sum of its entries. Le Van et al. (Ranked Tiling, 2014) already illustrated its applicability to gene expression analysis and addressed it with a constraint programming (CP) approach combined with large neighborhood search (CP-LNS). In this work, we exhibit some key properties of this NP-hard problem and define a bounding function such that larger problems can be solved in reasonable time. Two different algorithms are proposed in order to exploit the highlighted characteristics of the problem: a CP approach with a global constraint (CPGC) and mixed integer linear programming (MILP). Practical experiments conducted both on synthetic and real gene expression data exhibit the characteristics of these approaches and their relative benefits over the original CP-LNS method. Overall, the CPGC approach tends to be the fastest to produce a good solution. Yet, the MILP formulation is arguably the easiest to formulate and can also be competitive.

We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve this integer program, we propose a column generation formulation where the pricing program is solved via exact optimization of very small scale integer programs. Column generation is tightened using odd set inequalities which fit elegantly into pricing problem optimization. Our column generation approach achieves fast stable anytime inference for our instance segmentation problems. We demonstrate on three distinct light microscopy datasets, with several hundred cells each, that our proposed algorithm rapidly achieves or exceeds state of the art accuracy. Keywords: Combinatorial optimization, Column generation, Integer programming, Large scale optimization, Linear programming 1. Introduction Cell detection and instance segmentation are fundamental tasks for the study of bioimages (Meijering, 2012) in the era of big data.

A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values to the variables. Depending on the type of constraints that we allow in the input, a CSP might be tractable, or computationally hard. In recent years, general criteria have been discovered that imply that a CSP is polynomial-time tractable, or that it is NP-hard. Finite-domain CSPs have become a major common research focus of graph theory, artificial intelligence, and finite model theory. It turned out that the key questions for complexity classification of CSPs are closely linked to central questions in universal algebra. This thesis studies CSPs where the variables can take values from an infinite domain. This generalization enhances dramatically the range of computational problems that can be modeled as a CSP. Many problems from areas that have so far seen no interaction with constraint satisfaction theory can be formulated using infinite domains, e.g. problems from temporal and spatial reasoning, phylogenetic reconstruction, and operations research. It turns out that the universal-algebraic approach can also be applied to study large classes of infinite-domain CSPs, yielding elegant complexity classification results. A new tool in this thesis that becomes relevant particularly for infinite domains is Ramsey theory. We demonstrate the feasibility of our approach with two complete complexity classification results: one on CSPs in temporal reasoning, the other on a generalization of Schaefer's theorem for propositional logic to logic over graphs. We also study the limits of complexity classification, and present classes of computational problems provably do not exhibit a complexity dichotomy into hard and easy problems.

The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.