Logistic Regression (LR) is a widely used statistical method in empirical binary classification studies. However, real-life scenarios oftentimes share complexities that prevent from the use of the as-is LR model, and instead highlight the need to include high-order interactions to capture data variability. This becomes even more challenging because of: (i) datasets growing wider, with more and more variables; (ii) studies being typically conducted in strongly imbalanced settings; (iii) samples going from very large to extremely small; (iv) the need of providing both predictive models and interpretable results. In this paper we present a novel algorithm, Learning high-order Interactions via targeted Pattern Search (LIPS), to select interaction terms of varying order to include in a LR model for an imbalanced binary classification task when input data are categorical. LIPS's rationale stems from the duality between item sets and categorical interactions. The algorithm relies on an interaction learning step based on a well-known frequent item set mining algorithm, and a novel dissimilarity-based interaction selection step that allows the user to specify the number of interactions to be included in the LR model. In addition, we particularize two variants (Scores LIPS and Clusters LIPS), that can address even more specific needs. Through a set of experiments we validate our algorithm and prove its wide applicability to real-life research scenarios, showing that it outperforms a benchmark state-of-the-art algorithm.

Online convex optimization is a framework where a learner sequentially queries an external data source in order to arrive at the optimal solution of a convex function. The paradigm has gained significant popularity recently thanks to its scalability in large-scale optimization and machine learning. The repeated interactions, however, expose the learner to privacy risks from eavesdropping adversary that observe the submitted queries. In this paper, we study how to optimally obfuscate the learner's queries in first-order online convex optimization, so that their learned optimal value is provably difficult to estimate for the eavesdropping adversary. We consider two formulations of learner privacy: a Bayesian formulation in which the convex function is drawn randomly, and a minimax formulation in which the function is fixed and the adversary's probability of error is measured with respect to a minimax criterion. We show that, if the learner wants to ensure the probability of accurate prediction by the adversary be kept below $1/L$, then the overhead in query complexity is additive in $L$ in the minimax formulation, but multiplicative in $L$ in the Bayesian formulation. Compared to existing learner-private sequential learning models with binary feedback, our results apply to the significantly richer family of general convex functions with full-gradient feedback. Our proofs are largely enabled by tools from the theory of Dirichlet processes, as well as more sophisticated lines of analysis aimed at measuring the amount of information leakage under a full-gradient oracle.

In recent years, to improve the evolutionary algorithms used to solve optimization problems involving a large number of decision variables, many attempts have been made to simplify the problem solution space of a given problem for the evolutionary search. In the literature, the existing approaches can generally be categorized as decomposition-based methods and dimension-reduction-based methods. The former decomposes a large-scale problem into several smaller subproblems, while the latter transforms the original high-dimensional solution space into a low-dimensional space. However, it is worth noting that a given large-scale optimization problem may not always be decomposable, and it is also difficult to guarantee that the global optimum of the original problem is preserved in the reduced low-dimensional problem space. This paper thus proposes a new search paradigm, namely the multi-space evolutionary search, to enhance the existing evolutionary search methods for solving large-scale optimization problems. In contrast to existing approaches that perform an evolutionary search in a single search space, the proposed paradigm is designed to conduct a search in multiple solution spaces that are derived from the given problem, each possessing a unique landscape. The proposed paradigm makes no assumptions about the large-scale optimization problem of interest, such as that the problem is decomposable or that a certain relationship exists among the decision variables. To verify the efficacy of the proposed paradigm, comprehensive empirical studies in comparison to four state-of-the-art algorithms were conducted using the CEC2013 large-scale benchmark problems.

In goal-oriented requirements engineering, goal conflict identification is of fundamental importance for requirements analysis. The task aims to find the feasible situations which make the goals diverge within the domain, called boundary conditions (BCs). However, the existing approaches for goal conflict identification fail to find sufficient BCs and general BCs which cover more combinations of circumstances. From the BCs found by these existing approaches, we have observed an interesting phenomenon that there are some pairs of BCs are similar in formula structure, which occurs frequently in the experimental cases. In other words, once a BC is found, a new BC may be discovered quickly by slightly changing the former. It inspires us to develop a local search algorithm named LOGION to find BCs, in which the structural similarity is captured by the neighborhood relation of formulae. Based on structural similarity, LOGION can find a lot of BCs in a short time. Moreover, due to the large number of BCs identified, it potentially selects more general BCs from them. By taking experiments on a set of cases, we show that LOGION effectively exploits the structural similarity of BCs. We also compare our algorithm against the two state-of-the-art approaches. The experimental results show that LOGION produces one order of magnitude more BCs than the state-of-the-art approaches and confirm that LOGION finds out more general BCs thanks to a large number of BCs.

It is argued that a broad class of AGI-relevant algorithms can be expressed in a common formal framework, via specifying Galois connections linking search and optimization processes on directed metagraphs whose edge targets are labeled with probabilistic dependent types, and then showing these connections are fulfilled by processes involving metagraph chronomorphisms. Examples are drawn from the core cognitive algorithms used in the OpenCog AGI framework: Probabilistic logical inference, evolutionary program learning, pattern mining, agglomerative clustering, pattern mining and nonlinear-dynamical attention allocation. The analysis presented involves representing these cognitive algorithms as recursive discrete decision processes involving optimizing functions defined over metagraphs, in which the key decisions involve sampling from probability distributions over metagraphs and enacting sets of combinatory operations on selected sub-metagraphs. The mutual associativity of the combinatory operations involved in a cognitive process is shown to often play a key role in enabling the decomposition of the process into folding and unfolding operations; a conclusion that has some practical implications for the particulars of cognitive processes, e.g. militating toward use of reversible logic and reversible program execution. It is also observed that where this mutual associativity holds, there is an alignment between the hierarchy of subgoals used in recursive decision process execution and a hierarchy of subpatterns definable in terms of formal pattern theory.

This paper proposes a novel cell-based neural architecture search algorithm (NAS), which completely alleviates the expensive costs of data labeling inherited from supervised learning. Our algorithm capitalizes on the effectiveness of self-supervised learning for image representations, which is an increasingly crucial topic of computer vision. First, using only a small amount of unlabeled train data under contrastive self-supervised learning allow us to search on a more extensive search space, discovering better neural architectures without surging the computational resources. Second, we entirely relieve the cost for labeled data (by contrastive loss) in the search stage without compromising architectures' final performance in the evaluation phase. Finally, we tackle the inherent discrete search space of the NAS problem by sequential model-based optimization via the tree-parzen estimator (SMBO-TPE), enabling us to reduce the computational expense response surface significantly. An extensive number of experiments empirically show that our search algorithm can achieve state-of-the-art results with better efficiency in data labeling cost, searching time, and accuracy in final validation.

In this paper, we explore and compare multiple algorithms for solving the complex strategy game of Terra Mystica, hereafter abbreviated as TM. Previous work in the area of super-human game-play using AI has proven effective, with recent break-through for generic algorithms in games such as Go, Chess, and Shogi \cite{AlphaZero}. We directly apply these breakthroughs to a novel state-representation of TM with the goal of creating an AI that will rival human players. Specifically, we present the initial results of applying AlphaZero to this state-representation and analyze the strategies developed. A brief analysis is presented. We call this modified algorithm with our novel state-representation AlphaTM. In the end, we discuss the success and shortcomings of this method by comparing against multiple baselines and typical human scores. All code used for this paper is available at on \href{https://github.com/kandluis/terrazero}{GitHub}.

Finding exact circuit size is a notorious optimization problem in practice. Whereas modern computers and algorithmic techniques allow to find a circuit of size seven in blink of an eye, it may take more than a week to search for a circuit of size thirteen. One of the reasons of this behavior is that the search space is enormous: the number of circuits of size $s$ is $s^{\Theta(s)}$, the number of Boolean functions on $n$ variables is $2^{2^n}$. In this paper, we explore the following natural heuristic idea for decreasing the size of a given circuit: go through all its subcircuits of moderate size and check whether any of them can be improved by reducing to SAT. This may be viewed as a local search approach: we search for a smaller circuit in a ball around a given circuit. We report the results of experiments with various symmetric functions.

In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically the information bottleneck (IB) method, to pose a graph abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints, and are not provided to the system a priori. We detail our formulation and show how the problem can be realized as an integer linear program. A non-trivial numerical example is presented to demonstrate the utility in employing our approach to obtain hierarchical tree abstractions for resource-limited agents.

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.