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Register a new userMultidataset Independent Subspace Analysis with Application to Multimodal Fusion
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In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of information available in multiple datasets. Multidatasets, on the other hand, yield joint solutions otherwise unavailable in isolation, with a potential for pivotal insights into complex systems. To take advantage of the complex multidimensional subspace structures that capture underlying modes of shared and unique variability across and within datasets, we present a direct, principled approach to multidataset combination. We design a new method called multidataset independent subspace analysis (MISA) that leverages joint information from multiple heterogeneous datasets in a flexible and synergistic fashion. Methodological innovations exploiting the Kotz distribution for subspace modeling in conjunction with a novel combinatorial optimization for evasion of local minima enable MISA to produce a robust generalization of independent component analysis (ICA), independent vector analysis (IVA), and independent subspace analysis (ISA) in a single unified model. We highlight the utility of MISA for multimodal information fusion, including sample-poor regimes and low signal-to-noise ratio scenarios, promoting novel applications in both unimodal and multimodal brain imaging data.
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Due to its high computational speed and accuracy compared to ab-initio quantum chemistry and forcefield modeling, the prediction of molecular properties using machine learning has received great attention in the fields of materials design and drug discovery. A main ingredient required for machine learning is a training dataset consisting of molecular featurestextemdash for example fingerprint bits, chemical descriptors, etc. that adequately characterize the corresponding molecules. However, choosing features for any application is highly non-trivial. No universal method for feature selection exists. In this work, we propose a data fusion framework that uses Independent Vector Analysis to exploit underlying complementary information contained in different molecular featurization methods, bringing us a step closer to automated feature generation. Our approach takes an arbitrary number of individual feature vectors and automatically generates a single, compact (low dimensional) set of molecular features that can be used to enhance the prediction performance of regression models. At the same time our methodology retains the possibility of interpreting the generated features to discover relationships between molecular structures and properties. We demonstrate this on the QM7b dataset for the prediction of several properties such as atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. In addition, we show how our method helps improve the prediction of experimental binding affinities for a set of human BACE-1 inhibitors. To encourage more widespread use of IVA we have developed the PyIVA Python package, an open source code which is available for download on Github.
Metric elicitation is a recent framework for eliciting performance metrics that best reflect implicit user preferences. This framework enables a practitioner to adjust the performance metrics based on the application, context, and population at hand. However, available elicitation strategies have been limited to linear (or fractional-linear) functions of predictive rates. In this paper, we develop an approach to elicit from a wider range of complex multiclass metrics defined by quadratic functions of rates by exploiting their local linear structure. We apply this strategy to elicit quadratic metrics for group-based fairness, and also discuss how it can be generalized to higher-order polynomials. Our elicitation strategies require only relative preference feedback and are robust to both feedback and finite sample noise.
The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the dynamics, is almost always assumed to be additive. Additivity greatly limits the generality of the model, hindering analysis of general NVAR processes which have nonlinear interactions between the innovations. Here, we propose a new general framework called independent innovation analysis (IIA), which estimates the innovations from completely general NVAR. We assume mutual independence of the innovations as well as their modulation by an auxiliary variable (which is often taken as the time index and simply interpreted as nonstationarity). We show that IIA guarantees the identifiability of the innovations with arbitrary nonlinearities, up to a permutation and component-wise invertible nonlinearities. We also propose three estimation frameworks depending on the type of the auxiliary variable. We thus provide the first rigorous identifiability result for general NVAR, as well as very general tools for learning such models.
Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with nonsmooth and nonconvex objective. Such an optimization problem is very challenging to solve. Existing methods usually solve its convex relaxation or need to smooth its nonsmooth part using certain smoothing techniques. In this paper, we propose a manifold proximal linear method (ManPL) that solves the original SSC formulation. We also extend the algorithm to solve the multiple-kernel SSC problems, for which an alternating ManPL algorithm is proposed. Convergence and iteration complexity results of the proposed methods are established. We demonstrate the advantage of our proposed methods over existing methods via the single-cell RNA sequencing data analysis.
In multimodal sentiment analysis (MSA), the performance of a model highly depends on the quality of synthesized embeddings. These embeddings are generated from the upstream process called multimodal fusion, which aims to extract and combine the input unimodal raw data to produce a richer multimodal representation. Previous work either back-propagates the task loss or manipulates the geometric property of feature spaces to produce favorable fusion results, which neglects the preservation of critical task-related information that flows from input to the fusion results. In this work, we propose a framework named MultiModal InfoMax (MMIM), which hierarchically maximizes the Mutual Information (MI) in unimodal input pairs (inter-modality) and between multimodal fusion result and unimodal input in order to maintain task-related information through multimodal fusion. The framework is jointly trained with the main task (MSA) to improve the performance of the downstream MSA task. To address the intractable issue of MI bounds, we further formulate a set of computationally simple parametric and non-parametric methods to approximate their truth value. Experimental results on the two widely used datasets demonstrate the efficacy of our approach. The implementation of this work is publicly available at https://github.com/declare-lab/Multimodal-Infomax.
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