Rank-based Decomposable Losses in Machine Learning: A Survey

Recent works have revealed an essential paradigm in designing loss functions that differentiate individual losses vs. aggregate losses. The individual loss measures the quality of the model on a sample, while the aggregate loss combines individual losses/scores over each training sample. Both have a common procedure that aggregates a set of individual values to a single numerical value. The ranking order reflects the most fundamental relation among individual values in designing losses. In addition, decomposability, in which a loss can be decomposed into an ensemble of individual terms, becomes a significant property of organizing losses/scores. This survey provides a systematic and comprehensive review of rank-based decomposable losses in machine learning. Specifically, we provide a new taxonomy of loss functions that follows the perspectives of aggregate loss and individual loss. We identify the aggregator to form such losses, which are examples of set functions. We organize the rank-based decomposable losses into eight categories. Following these categories, we review the literature on rank-based aggregate losses and rank-based individual losses. We describe general formulas for these losses and connect them with existing research topics. We also suggest future research directions spanning unexplored, remaining, and emerging issues in rank-based decomposable losses.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI

A Speaker Verification Backend with Robust Performance across Conditions

In this paper, we address the problem of speaker verification in conditions unseen or unknown during development. A standard method for speaker verification consists of extracting speaker embeddings with a deep neural network and processing them through a backend composed of probabilistic linear discriminant analysis (PLDA) and global logistic regression score calibration. This method is known to result in systems that work poorly on conditions different from those used to train the calibration model. We propose to modify the standard backend, introducing an adaptive calibrator that uses duration and other automatically extracted side-information to adapt to the conditions of the inputs. The backend is trained discriminatively to optimize binary cross-entropy. When trained on a number of diverse datasets that are labeled only with respect to speaker, the proposed backend consistently and, in some cases, dramatically improves calibration, compared to the standard PLDA approach, on a number of held-out datasets, some of which are markedly different from the training data. Discrimination performance is also consistently improved. We show that joint training of the PLDA and the adaptive calibrator is essential -- the same benefits cannot be achieved when freezing PLDA and fine-tuning the calibrator. To our knowledge, the results in this paper are the first evidence in the literature that it is possible to develop a speaker verification system with robust out-of-the-box performance on a large variety of conditions

Structured Sparse Methods for Imaging Genetics

abstract: Imaging genetics is an emerging and promising technique that investigates how genetic variations affect brain development, structure, and function. By exploiting disorder-related neuroimaging phenotypes, this class of studies provides a novel direction to reveal and understand the complex genetic mechanisms. Oftentimes, imaging genetics studies are challenging due to the relatively small number of subjects but extremely high-dimensionality of both imaging data and genomic data. In this dissertation, I carry on my research on imaging genetics with particular focuses on two tasks---building predictive models between neuroimaging data and genomic data, and identifying disorder-related genetic risk factors through image-based biomarkers. To this end, I consider a suite of structured sparse methods---that can produce interpretable models and are robust to overfitting---for imaging genetics. With carefully-designed sparse-inducing regularizers, different biological priors are incorporated into learning models. More specifically, in the Allen brain image--gene expression study, I adopt an advanced sparse coding approach for image feature extraction and employ a multi-task learning approach for multi-class annotation. Moreover, I propose a label structured-based two-stage learning framework, which utilizes the hierarchical structure among labels, for multi-label annotation. In the Alzheimer's disease neuroimaging initiative (ADNI) imaging genetics study, I employ Lasso together with EDPP (enhanced dual polytope projections) screening rules to fast identify Alzheimer's disease risk SNPs. I also adopt the tree-structured group Lasso with MLFre (multi-layer feature reduction) screening rules to incorporate linkage disequilibrium information into modeling. Moreover, I propose a novel absolute fused Lasso model for ADNI imaging genetics. This method utilizes SNP spatial structure and is robust to the choice of reference alleles of genotype coding. In addition, I propose a two-level structured sparse model that incorporates gene-level networks through a graph penalty into SNP-level model construction. Lastly, I explore a convolutional neural network approach for accurate predicting Alzheimer's disease related imaging phenotypes. Experimental results on real-world imaging genetics applications demonstrate the efficiency and effectiveness of the proposed structured sparse methods.Dissertation/ThesisDoctoral Dissertation Computer Science 201

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

SOME CONTRIBUTIONS TO DATA DRIVEN INDIVIDUALIZED DECISION MAKING PROBLEMS

Recent exploration of the optimal individualized decision rule (IDR) for patients in precision medicine has attracted a lot of attentions due to the potential heterogeneous response of patients to different treatments. In the current literature, an optimal IDR is a decision function based on patients’ characteristics for the treatment that maximizes the expected outcome. My dissertation research mainly focuses on how to estimate optimal IDRs under various criteria given experimental data. In the first part of this dissertation, focusing on maximizing expected outcome, we propose an angle-based direct learning (AD-learning) method to efficiently estimate optimal IDRs with multiple treatments for various types of outcomes. This contributes to the literature, where many existing methods are designed for binary treatment settings with the interest of a continuous outcome. In the second part, motivated by complex individualized decision making procedures, we propose two new robust criteria to estimate optimal IDRs: one is to control the average lower tail of the subjects’ outcomes and the other is to control the individualized lower tail of each subject’s outcome. In addition to optimizing the individualized expected outcome, our proposed criteria take risks into consideration, and thus the resulting IDRs can prevent adverse events caused by the heavy lower tail of the outcome distribution. In the third part of this dissertation, motivated by the concept of Optimized Certainty Equivalent (OCE), we generalize the second part and propose a decision-rule based optimized covariates dependent equivalent (CDE) for individualized decision making problems. Our proposed IDR-CDE not only broadens the existing expected outcome framework in precision medicine but also enriches the previous concept of the OCE in the risk management. We study the related mathematical problem of estimating an optimal IDRs both theoretically and numerically.Doctor of Philosoph