The challenge in biomarker discovery using machine learning from omics data lies in the abundance of molecular features but scarcity of samples. Most feature selection methods in machine learning require evaluating various sets of features (models) to determine the most effective combination. This process, typically conducted using a validation dataset, involves testing different feature sets to optimize the model's performance. Evaluations have performance estimation error and when the selection involves many models the best ones are almost certainly overestimated. Biomarker identification with feature selection methods can be addressed as a multi-objective problem with trade-offs between predictive ability and parsimony in the number of features. Genetic algorithms are a popular tool for multi-objective optimization but they evolve numerous solutions thus are prone to overestimation. Methods have been proposed to reduce the overestimation after a model has already been selected in single-objective problems, but no algorithm existed capable of reducing the overestimation during the optimization, improving model selection, or applied in the more general multi-objective domain. We propose DOSA-MO, a novel multi-objective optimization wrapper algorithm that learns how the original estimation, its variance, and the feature set size of the solutions predict the overestimation. DOSA-MO adjusts the expectation of the performance during the optimization, improving the composition of the solution set. We verify that DOSA-MO improves the performance of a state-of-the-art genetic algorithm on left-out or external sample sets, when predicting cancer subtypes and/or patient overall survival, using three transcriptomics datasets for kidney and breast cancer.
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One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.
We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is based on the stretch energy functional, and the minimization is constrained on a power manifold of unit spheres embedded in 3-dimensional Euclidean space. Numerical experiments on several mesh models demonstrate the accuracy and stability of the proposed framework. Comparisons with two existing state-of-the-art methods for computing area-preserving mappings demonstrate that our algorithm is both competitive and more efficient. Finally, we present a concrete application to the problem of landmark-aligned surface registration of two brain models.
The standard approach to tackling computer vision problems is to train deep convolutional neural network (CNN) models using large-scale image datasets which are representative of the target task. However, in many scenarios, it is often challenging to obtain sufficient image data for the target task. Data augmentation is a way to mitigate this challenge. A common practice is to explicitly transform existing images in desired ways so as to create the required volume and variability of training data necessary to achieve good generalization performance. In situations where data for the target domain is not accessible, a viable workaround is to synthesize training data from scratch--i.e., synthetic data augmentation. This paper presents an extensive review of synthetic data augmentation techniques. It covers data synthesis approaches based on realistic 3D graphics modeling, neural style transfer (NST), differential neural rendering, and generative artificial intelligence (AI) techniques such as generative adversarial networks (GANs) and variational autoencoders (VAEs). For each of these classes of methods, we focus on the important data generation and augmentation techniques, general scope of application and specific use-cases, as well as existing limitations and possible workarounds. Additionally, we provide a summary of common synthetic datasets for training computer vision models, highlighting the main features, application domains and supported tasks. Finally, we discuss the effectiveness of synthetic data augmentation methods. Since this is the first paper to explore synthetic data augmentation methods in great detail, we are hoping to equip readers with the necessary background information and in-depth knowledge of existing methods and their attendant issues.
This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine the Bayesian regret analysis for posterior sampling reinforcement learning (PSRL), presenting an upper bound of ${\mathcal{O}}(d\sqrt{H^3 T \log T})$, where $d$ represents the dimensionality of the transition kernel, $H$ the planning horizon, and $T$ the total number of interactions. This signifies a methodological enhancement by optimizing the $\mathcal{O}(\sqrt{\log T})$ factor over the previous benchmark (Osband and Van Roy, 2014) specified to linear mixture MDPs. Our approach, leveraging a value-targeted model learning perspective, introduces a decoupling argument and a variance reduction technique, moving beyond traditional analyses reliant on confidence sets and concentration inequalities to formalize Bayesian regret bounds more effectively.
This work presents the cubature scheme for the fitting of spatio-temporal Poisson point processes. The methodology is implemented in the R Core Team (2024) package stopp (D'Angelo and Adelfio, 2023), published on the Comprehensive R Archive Network (CRAN) and available from //CRAN.R-project.org/package=stopp. Since the number of dummy points should be sufficient for an accurate estimate of the likelihood, numerical experiments are currently under development to give guidelines on this aspect.
Compared to other techniques, particle swarm optimization is more frequently utilized because of its ease of use and low variability. However, it is complicated to find the best possible solution in the search space in large-scale optimization problems. Moreover, changing algorithm variables does not influence algorithm convergence much. The PSO algorithm can be combined with other algorithms. It can use their advantages and operators to solve this problem. Therefore, this paper proposes the onlooker multi-parent crossover discrete particle swarm optimization (OMPCDPSO). To improve the efficiency of the DPSO algorithm, we utilized multi-parent crossover on the best solutions. We performed an independent and intensive neighborhood search using the onlooker bees of the bee algorithm. The algorithm uses onlooker bees and crossover. They do local search (exploitation) and global search (exploration). Each of these searches is among the best solutions (employed bees). The proposed algorithm was tested on the allocation problem, which is an NP-hard optimization problem. Also, we used two types of simulated data. They were used to test the scalability and complexity of the better algorithm. Also, fourteen 2D test functions and thirteen 30D test functions were used. They also used twenty IEEE CEC2005 benchmark functions to test the efficiency of OMPCDPSO. Also, to test OMPCDPSO's performance, we compared it to four new binary optimization algorithms and three classic ones. The results show that the OMPCDPSO version had high capability. It performed better than other algorithms. The developed algorithm in this research (OMCDPSO) in 36 test functions out of 47 (76.60%) is better than other algorithms. The Onlooker bees and multi-parent operators significantly impact the algorithm's performance.
Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.
Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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