Variational Inference (VI) optimizes varia- tional parameters to closely align a variational distribution with the true posterior, being ap- proached through vanilla gradient descent in black-box VI or natural-gradient descent in natural-gradient VI. In this work, we reframe VI as the optimization of an objective that concerns probability distributions defined over a variational parameter space. Subsequently, we propose Wasserstein gradient descent for solving this optimization, where black-box VI and natural-gradient VI can be interpreted as special cases of the proposed Wasserstein gradient descent. To enhance the efficiency of optimization, we develop practical methods for numerically solving the discrete gradient flows. We validate the effectiveness of the pro- posed methods through experiments on syn- thetic and real-world datasets, supplemented by theoretical analyses.

We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, we propose an iterative particle-based algorithm, which we call Muliple Wasserstein Gradient Descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective functional based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, we provide theoretical analysis and present experimental results on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.

MOTIVATION: Metabolomics involves studies of a great number of metabolites, which are small molecules present in biological systems. They play a lot of important functions such as energy transport, signaling, building block of cells and inhibition/catalysis. Understanding biochemical characteristics of the metabolites is an essential and significant part of metabolomics to enlarge the knowledge of biological systems. It is also the key to the development of many applications and areas such as biotechnology, biomedicine or pharmaceuticals. However, the identification of the metabolites remains a challenging task in metabolomics with a huge number of potentially interesting but unknown metabolites. The standard method for identifying metabolites is based on the mass spectrometry (MS) preceded by a separation technique. Over many decades, many techniques with different approaches have been proposed for MS-based metabolite identification task, which can be divided into the following four groups: mass spectra database, in silico fragmentation, fragmentation tree and machine learning. In this review paper, we thoroughly survey currently available tools for metabolite identification with the focus on in silico fragmentation, and machine learning-based approaches. We also give an intensive discussion on advanced machine learning methods, which can lead to further improvement on this task.

MOTIVATION: Metabolite identification is an important task in metabolomics to enhance the knowledge of biological systems. There have been a number of machine learning-based methods proposed for this task, which predict a chemical structure of a given spectrum through an intermediate (chemical structure) representation called molecular fingerprints. They usually have two steps: (i) predicting fingerprints from spectra; (ii) searching chemical compounds (in database) corresponding to the predicted fingerprints. Fingerprints are feature vectors, which are usually very large to cover all possible substructures and chemical properties, and therefore heavily redundant, in the sense of having many molecular (sub)structures irrelevant to the task, causing limited predictive performance and slow prediction. RESULTS: We propose ADAPTIVE, which has two parts: learning two mappings (i) from structures to molecular vectors and (ii) from spectra to molecular vectors. The first part learns molecular vectors for metabolites from given data, to be consistent with both spectra and chemical structures of metabolites. In more detail, molecular vectors are generated by a model, being parameterized by a message passing neural network, and parameters are estimated by maximizing the correlation between molecular vectors and the corresponding spectra in terms of Hilbert-Schmidt Independence Criterion. Molecular vectors generated by this model are compact and importantly adaptive (specific) to both given data and task of metabolite identification. The second part uses input output kernel regression (IOKR), the current cutting-edge method of metabolite identification. We empirically confirmed the effectiveness of ADAPTIVE by using a benchmark data, where ADAPTIVE outperformed the original IOKR in both predictive performance and computational efficiency. AVAILABILITY AND IMPLEMENTATION: The code will be accessed through http://www.bic.kyoto-u.ac.jp/pathway/tools/ADAPTIVE after the acceptance of this article.

Motivation: Recent success in metabolite identification from tandem mass spectra has been led by machine learning, which has two stages: mapping mass spectra to molecular fingerprint vectors and then retrieving candidate molecules from the database. In the first stage, i.e. fingerprint prediction, spectrum peaks are features and considering their interactions would be reasonable for more accurate identification of unknown metabolites. Existing approaches of fingerprint prediction are based on only individual peaks in the spectra, without explicitly considering the peak interactions. Also the current cutting-edge method is based on kernels, which are computationally heavy and difficult to interpret. Results: We propose two learning models that allow to incorporate peak interactions for fingerprint prediction. First, we extend the state-of-the-art kernel learning method by developing kernels for peak interactions to combine with kernels for peaks through multiple kernel learning (MKL). Second, we formulate a sparse interaction model for metabolite peaks, which we call SIMPLE, which is computationally light and interpretable for fingerprint prediction. The formulation of SIMPLE is convex and guarantees global optimization, for which we develop an alternating direction method of multipliers (ADMM) algorithm. Experiments using the MassBank dataset show that both models achieved comparative prediction accuracy with the current top-performance kernel method. Furthermore SIMPLE clearly revealed individual peaks and peak interactions which contribute to enhancing the performance of fingerprint prediction. Availability and implementation: The code will be accessed through http://mamitsukalab.org/tools/SIMPLE/.