Tsetlin Machines (TMs) have garnered increasing interest for their ability to learn concepts via propositional formulas and their proven efficiency across various application domains. Despite this, the convergence proof for the TMs, particularly for the AND operator (conjunction of literals), in the generalized case (inputs greater than two bits) remains an open problem. This paper aims to fill this gap by presenting a comprehensive convergence analysis of Tsetlin automaton-based Machine Learning algorithms. We introduce a novel framework, referred to as Probabilistic Concept Learning (PCL), which simplifies the TM structure while incorporating dedicated feedback mechanisms and dedicated inclusion/exclusion probabilities for literals. Given n features, PCL aims to learn a set of conjunction clauses Ci each associated with a distinct inclusion probability pi. Most importantly, we establish a theoretical proof confirming that, for any clause k, PCL converges to a conjunction of literals when pk is between 0.5 and 1. This result serves as a stepping stone for future research on the convergence properties of Tsetlin automaton-based learning algorithms. Our findings not only contribute to the theoretical understanding of Tsetlin automaton-based learning algorithms but also have implications for their practical application, potentially leading to more robust and interpretable machine learning models.

This study introduces deep learning (DL) methods for imputing missing allele-frequency information in large-scale genome-wide pooled re-sequencing (Pool-Seq) data, using the comprehensive DEST dataset based on over 270 global samples of the vinegar fly Drosophila melanogaster as a use case. The primary challenge addressed here is gap filling in DNA sequences, a critical issue in large-scale genomic studies. An empirical baseline for missing allele frequencies was established using an inverse-distance-weighting (IDW) method, leveraging geographical and temporal proximity among densely sampled populations. Additionally, a machine learning (ML) approach with k-means clustering grouped populations based on allele frequencies, independent of their spatiotemporal context. The core contribution of this research is the application of advanced DL models, specifically Masked Autoencoders (MAE), Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN). These models excel in learning the data distribution and generating plausible imputations for missing sequences, outperforming the IDW and k-means based methods. Their effectiveness is due to their ability to handle high-dimensional genetic sequences and capture complex data correlations while maintaining sequential integrity. The study demonstrates the efficacy of DL in genomic data analysis, particularly for large-scale, complex datasets. VAE and GAN models offer a significant advancement over traditional ML methods, providing more accurate and efficient solutions for gap filling in genetic sequences. This research highlights the potential of DL in genomics, setting a precedent for future AI applications in biological data analysis and demonstrating a novel application area for deep learning techniques in handling complex long-sequence biological datasets.

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. Recently, we introduced GEQCA-I, which stands for Generic Qualitative Constraint Acquisition, as a new active constraint acquisition method for learning qualitative constraints using qualitative queries. In this paper, we revise and extend GEQCA-I to GEQCA-II with a new type of query, universal query, for qualitative constraint acquisition, with a deeper query-driven acquisition algorithm. Our extended experimental evaluation shows the efficiency and usefulness of the concept of universal query in learning randomly-generated qualitative networks, including both temporal networks based on Allen’s algebra and spatial networks based on region connection calculus. We also show the effectiveness of GEQCA-II in learning the qualitative part of real scheduling problems.

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. On the one hand, the precise modelling of these constraints, which are formulated in various relation algebras, entails a number of possible logical combinations and requires expertise in constraint-based modelling. On the other hand, active constraint acquisition (CA) has been used successfully to support non-experienced users in learning conjunctive constraint networks through the generation of a sequence of queries. In this paper, we propose GEACQ, which stands for Generic Qualitative Constraint Acquisition, an active CA method that learns qualitative constraints via the concept of qualitative queries. GEACQ combines qualitative queries with time-bounded path consistency (PC) and background knowledge propagation to acquire the qualitative constraints of any scheduling or packing problem. We prove soundness, completeness and termination of GEACQ by exploiting the jointly exhaustive and pairwise disjoint property of qualitative calculus and we give an experimental evaluation that shows (i) the efficiency of our approach in learning temporal constraints and, (ii) the use of GEACQ on real scheduling instances.

The problem of discovering frequent itemsets including rare ones has received a great deal of attention. The mining process needs to be flexible enough to extract frequent and rare regularities at once. On the other hand, it has recently been shown that constraint programming is a flexible way to tackle data mining tasks. In this paper, we propose a constraint programming approach for mining itemsets with multiple minimum supports. Our approach provides the user with the possibility to express any kind of constraints on the minimum item supports. An experimental analysis shows the practical effectiveness of our approach compared to the state of the art.

Frequent itemset mining is one of the most studied tasks in knowledge discovery. It is often reduced to mining the positive border of frequent itemsets, i.e. maximal frequent itemsets. Infrequent itemset mining, on the other hand, can be reduced to mining the negative border, i.e. minimal infrequent itemsets. We propose a generic framework based on constraint programming to mine both borders of frequent itemsets.One can easily decide which border to mine by setting a simple parameter. For this, we introduce two new global constraints, FREQUENTSUBS and INFREQUENTSUPERS, with complete polynomial propagators. We then consider the problem of mining borders with additional constraints. We prove that this problem is coNP-hard, ruling out the hope for the existence of a single CSP solving this problem (unless coNP ⊆ NP).

Discovering association rules among items in a dataset is one of the fundamental problems in data mining. It has recently been shown that constraint programming is a flexible way to tackle data mining tasks. In this paper we propose a declarative model based on constraint programming to capture association rules. Our model also allows us to specify any additional property and/or user's constraints on the kind of rules the user is looking for. To implement our model, we introduce a new global constraint, Confident, for ensuring the confidence of rules. We prove that completely propagating Confident is NP-hard. We thus provide a decomposition of Confident. In addition to user's constraints on the items composing body and head of the rules, we show that we can capture the popular minimal non-redundant property of association rules. An experimental analysis shows the practical effectiveness of our approach compared to existing approaches.