In this work, we study $\gamma$-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG). The framework directly integrates dynamic programming with (any) policy gradient method, explicitly leveraging the Markovian property of the environment. DynPG dynamically adjusts the problem horizon during training, decomposing the original infinite-horizon MDP into a sequence of contextual bandit problems. By iteratively solving these contextual bandits, DynPG converges to the stationary optimal policy of the infinite-horizon MDP. To demonstrate the power of DynPG, we establish its non-asymptotic global convergence rate under the tabular softmax parametrization, focusing on the dependencies on salient but essential parameters of the MDP. By combining classical arguments from dynamic programming with more recent convergence arguments of policy gradient schemes, we prove that softmax DynPG scales polynomially in the effective horizon $(1-\gamma)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.

In this paper, we aim to address a significant challenge in the field of missing data imputation: identifying and leveraging the interdependencies among features to enhance missing data imputation for tabular data. We introduce a novel framework named the Bipartite and Complete Directed Graph Neural Network (BCGNN). Within BCGNN, observations and features are differentiated as two distinct node types, and the values of observed features are converted into attributed edges linking them. The bipartite segment of our framework inductively learns embedding representations for nodes, efficiently utilizing the comprehensive information encapsulated in the attributed edges. In parallel, the complete directed graph segment adeptly outlines and communicates the complex interdependencies among features. When compared to contemporary leading imputation methodologies, BCGNN consistently outperforms them, achieving a noteworthy average reduction of 15% in mean absolute error for feature imputation tasks under different missing mechanisms. Our extensive experimental investigation confirms that an in-depth grasp of the interdependence structure substantially enhances the model's feature embedding ability. We also highlight the model's superior performance in label prediction tasks involving missing data, and its formidable ability to generalize to unseen data points.

Recent AI advances have enabled multi-modal systems to model and translate diverse information spaces. Extending beyond text and vision, we introduce OneProt, a multi-modal AI for proteins that integrates structural, sequence, alignment, and binding site data. Using the ImageBind framework, OneProt aligns the latent spaces of modality encoders along protein sequences. It demonstrates strong performance in retrieval tasks and surpasses state-of-the-art methods in various downstream tasks, including metal ion binding classification, gene-ontology annotation, and enzyme function prediction. This work expands multi-modal capabilities in protein models, paving the way for applications in drug discovery, biocatalytic reaction planning, and protein engineering.

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual Hamiltonian and a map from the original to the dual observables. By using simple neural networks to parameterize these maps and introducing a loss function that penalises the difference between correlation functions in original and dual models, we formulate the process of duality discovery as an optimization problem. We numerically solve this problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model, reconstructing the known mapping of temperatures. We also discuss an alternative approach which uses known features of the mapping of topological lines to reduce the problem to optimizing the couplings in a dual Hamiltonian, and explore next-to-nearest neighbour deformations of the 2d Ising duality. We discuss future directions and prospects for discovering new dualities within this framework.

Multi-objective reinforcement learning (MORL) is used to solve problems involving multiple objectives. An MORL agent must make decisions based on the diverse signals provided by distinct reward functions. Training an MORL agent yields a set of solutions (policies), each presenting distinct trade-offs among the objectives (expected returns). MORL enhances explainability by enabling fine-grained comparisons of policies in the solution set based on their trade-offs as opposed to having a single policy. However, the solution set is typically large and multi-dimensional, where each policy (e.g., a neural network) is represented by its objective values. We propose an approach for clustering the solution set generated by MORL. By considering both policy behavior and objective values, our clustering method can reveal the relationship between policy behaviors and regions in the objective space. This approach can enable decision makers (DMs) to identify overarching trends and insights in the solution set rather than examining each policy individually. We tested our method in four multi-objective environments and found it outperformed traditional k-medoids clustering. Additionally, we include a case study that demonstrates its real-world application.

Due to a variety of reasons, such as privacy, data in the wild often misses the grouping information required for identifying minorities. On the other hand, it is known that machine learning models are only as good as the data they are trained on and, hence, may underperform for the under-represented minority groups. The missing grouping information presents a dilemma for responsible data scientists who find themselves in an unknown-unknown situation, where not only do they not have access to the grouping attributes but do not also know what groups to consider. This paper is an attempt to address this dilemma. Specifically, we propose a minority mining problem, where we find vectors in the attribute space that reveal potential groups that are under-represented and under-performing. Technically speaking, we propose a geometric transformation of data into a dual space and use notions such as the arrangement of hyperplanes to design an efficient algorithm for the problem in lower dimensions. Generalizing our solution to the higher dimensions is cursed by dimensionality. Therefore, we propose a solution based on smart exploration of the search space for such cases. We conduct comprehensive experiments using real-world and synthetic datasets alongside the theoretical analysis. Our experiment results demonstrate the effectiveness of our proposed solutions in mining the unknown, under-represented, and under-performing minorities.

Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model. The model is designed to jointly learn key low-dimensional structures, including the tangent space, the normal subspace, and the quadratic form that links the tangent space to a low-dimensional representation. We solve the proposed factorization model using an alternating minimization method, involving an in-depth investigation of nonlinear regression and projection subproblems. Theoretical properties of the quadratic projection problem and convergence characteristics of the alternating strategy are also investigated. To validate our approach, we conduct numerical experiments on synthetic and real-world datasets. Results demonstrate that our model outperforms existing methods, highlighting its robustness and efficacy in capturing core low-dimensional structures.

Building a corpus become an important topic in natural language processing (NLP) and especially for low resource languages (ex: AD), due to the importance that the corpus plays in the development of several tools, such as: Machine Translation Babaali and Salem [2022], Part of speech tagging Chiche and Yitagesu [2022], Named entities recognition Jarrar et al. [2022], etc. in particular with the emergence of techniques based on statistics, machine learning and deep learning. Who exploits this mass of information to develop, train and evaluate models. However, building a corpus is not an easy task Bakari et al. [2016]; it is extremely time-consuming and requires a lot of work, for the good reason that the volume and quality of the corpus are two important parameters. Despite the recent emergence of techniques that consume fewer resources, such as few-shot learning Tunstall et al. [2022]. Over the last few years, a lot of studies in NLP have focused on languages or variants of languages called low resources Mengoni and Santucci [2023]. This change of direction is mainly due to the emergence of social media such as Facebook, Twitter, RenRen, LinkedIn, Google+, and Tuenti, as a means of communication where people exchange messages and comments.

Robustness is a fundamental aspect for developing safe and trustworthy models, particularly when they are deployed in the open world. In this work we analyze the inherent capability of one-stage object detectors to robustly operate in the presence of out-of-distribution (OoD) data. Specifically, we propose a novel detection algorithm for detecting unknown objects in image data, which leverages the features extracted by the model from each sample. Differently from other recent approaches in the literature, our proposal does not require retraining the object detector, thereby allowing for the use of pretrained models. Our proposed OoD detector exploits the application of supervised dimensionality reduction techniques to mitigate the effects of the curse of dimensionality on the features extracted by the model. Furthermore, it utilizes high-resolution feature maps to identify potential unknown objects in an unsupervised fashion. Our experiments analyze the Pareto trade-off between the performance detecting known and unknown objects resulting from different algorithmic configurations and inference confidence thresholds. We also compare the performance of our proposed algorithm to that of logits-based post-hoc OoD methods, as well as possible fusion strategies. Finally, we discuss on the competitiveness of all tested methods against state-of-the-art OoD approaches for object detection models over the recently published Unknown Object Detection benchmark. The obtained results verify that the performance of avant-garde post-hoc OoD detectors can be further improved when combined with our proposed algorithm.

Graph Neural Networks (GNNs) have shown great promise in modeling relationships between nodes in a graph, but capturing higher-order relationships remains a challenge for large-scale networks. Previous studies have primarily attempted to utilize the information from higher-order neighbors in the graph, involving the incorporation of powers of the shift operator, such as the graph Laplacian or adjacency matrix. This approach comes with a trade-off in terms of increased computational and memory demands. Relying on graph spectral theory, we make a fundamental observation: the regular and the Hadamard power of the Laplacian matrix behave similarly in the spectrum. This observation has significant implications for capturing higher-order information in GNNs for various tasks such as node classification and semi-supervised learning. Consequently, we propose a novel graph convolutional operator based on the sparse Sobolev norm of graph signals. Our approach, known as Sparse Sobolev GNN (S2-GNN), employs Hadamard products between matrices to maintain the sparsity level in graph representations. S2-GNN utilizes a cascade of filters with increasing Hadamard powers to generate a diverse set of functions. We theoretically analyze the stability of S2-GNN to show the robustness of the model against possible graph perturbations. We also conduct a comprehensive evaluation of S2-GNN across various graph mining, semi-supervised node classification, and computer vision tasks. In particular use cases, our algorithm demonstrates competitive performance compared to state-of-the-art GNNs in terms of performance and running time.