Aurélie Lozano

Zuobai Zhang, Minghao Xu, Arian Jamasb et al.

Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein function or structure. Existing approaches usually pretrain protein language models on a large number of unlabeled amino acid sequences and then finetune the models with some labeled data in downstream tasks. Despite the effectiveness of sequence-based approaches, the power of pretraining on known protein structures, which are available in smaller numbers only, has not been explored for protein property prediction, though protein structures are known to be determinants of protein function. In this paper, we propose to pretrain protein representations according to their 3D structures. We first present a simple yet effective encoder to learn the geometric features of a protein. We pretrain the protein graph encoder by leveraging multiview contrastive learning and different self-prediction tasks. Experimental results on both function prediction and fold classification tasks show that our proposed pretraining methods outperform or are on par with the state-of-the-art sequence-based methods, while using much less pretraining data. Our implementation is available at https://github.com/DeepGraphLearning/GearNet.

Zuobai Zhang, Chuanrui Wang, Minghao Xu et al.

Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein functions. Recent sequence representation learning methods based on Protein Language Models (PLMs) excel in sequence-based tasks, but their direct adaptation to tasks involving protein structures remains a challenge. In contrast, structure-based methods leverage 3D structural information with graph neural networks and geometric pre-training methods show potential in function prediction tasks, but still suffers from the limited number of available structures. To bridge this gap, our study undertakes a comprehensive exploration of joint protein representation learning by integrating a state-of-the-art PLM (ESM-2) with distinct structure encoders (GVP, GearNet, CDConv). We introduce three representation fusion strategies and explore different pre-training techniques. Our method achieves significant improvements over existing sequence- and structure-based methods, setting new state-of-the-art for function annotation. This study underscores several important design choices for fusing protein sequence and structure information. Our implementation is available at https://github.com/DeepGraphLearning/ESM-GearNet.

Zuobai Zhang, Minghao Xu, Aurélie Lozano et al.

Self-supervised pre-training methods on proteins have recently gained attention, with most approaches focusing on either protein sequences or structures, neglecting the exploration of their joint distribution, which is crucial for a comprehensive understanding of protein functions by integrating co-evolutionary information and structural characteristics. In this work, inspired by the success of denoising diffusion models in generative tasks, we propose the DiffPreT approach to pre-train a protein encoder by sequence-structure joint diffusion modeling. DiffPreT guides the encoder to recover the native protein sequences and structures from the perturbed ones along the joint diffusion trajectory, which acquires the joint distribution of sequences and structures. Considering the essential protein conformational variations, we enhance DiffPreT by a method called Siamese Diffusion Trajectory Prediction (SiamDiff) to capture the correlation between different conformers of a protein. SiamDiff attains this goal by maximizing the mutual information between representations of diffusion trajectories of structurally-correlated conformers. We study the effectiveness of DiffPreT and SiamDiff on both atom- and residue-level structure-based protein understanding tasks. Experimental results show that the performance of DiffPreT is consistently competitive on all tasks, and SiamDiff achieves new state-of-the-art performance, considering the mean ranks on all tasks. Our implementation is available at https://github.com/DeepGraphLearning/SiamDiff.

Igor Melnyk, Aurelie Lozano, Payel Das et al.

Inverse protein folding, the process of designing sequences that fold into a specific 3D structure, is crucial in bio-engineering and drug discovery. Traditional methods rely on experimentally resolved structures, but these cover only a small fraction of protein sequences. Forward folding models like AlphaFold offer a potential solution by accurately predicting structures from sequences. However, these models are too slow for integration into the optimization loop of inverse folding models during training. To address this, we propose using knowledge distillation on folding model confidence metrics, such as pTM or pLDDT scores, to create a faster and end-to-end differentiable distilled model. This model can then be used as a structure consistency regularizer in training the inverse folding model. Our technique is versatile and can be applied to other design tasks, such as sequence-based protein infilling. Experimental results show that our method outperforms non-regularized baselines, yielding up to 3% improvement in sequence recovery and up to 45% improvement in protein diversity while maintaining structural consistency in generated sequences. Code is available at https://github.com/IBM/AFDistill

Payel Das, Subhajit Chaudhury, Elliot Nelson et al.

Efficient and accurate updating of knowledge stored in Large Language Models (LLMs) is one of the most pressing research challenges today. This paper presents Larimar - a novel, brain-inspired architecture for enhancing LLMs with a distributed episodic memory. Larimar's memory allows for dynamic, one-shot updates of knowledge without the need for computationally expensive re-training or fine-tuning. Experimental results on multiple fact editing benchmarks demonstrate that Larimar attains accuracy comparable to most competitive baselines, even in the challenging sequential editing setup, but also excels in speed - yielding speed-ups of 8-10x depending on the base LLM - as well as flexibility due to the proposed architecture being simple, LLM-agnostic, and hence general. We further provide mechanisms for selective fact forgetting, information leakage prevention, and input context length generalization with Larimar and show their effectiveness. Our code is available at https://github.com/IBM/larimar

Zuobai Zhang, Jiarui Lu, Vijil Chenthamarakshan et al.

Protein language models are a powerful tool for learning protein representations through pre-training on vast protein sequence datasets. However, traditional protein language models lack explicit structural supervision, despite its relevance to protein function. To address this issue, we introduce the integration of remote homology detection to distill structural information into protein language models without requiring explicit protein structures as input. We evaluate the impact of this structure-informed training on downstream protein function prediction tasks. Experimental results reveal consistent improvements in function annotation accuracy for EC number and GO term prediction. Performance on mutant datasets, however, varies based on the relationship between targeted properties and protein structures. This underscores the importance of considering this relationship when applying structure-aware training to protein function prediction tasks. Code and model weights are available at https://github.com/DeepGraphLearning/esm-s.

Zuobai Zhang, Pascal Notin, Yining Huang et al.

Designing novel functional proteins crucially depends on accurately modeling their fitness landscape. Given the limited availability of functional annotations from wet-lab experiments, previous methods have primarily relied on self-supervised models trained on vast, unlabeled protein sequence or structure datasets. While initial protein representation learning studies solely focused on either sequence or structural features, recent hybrid architectures have sought to merge these modalities to harness their respective strengths. However, these sequence-structure models have so far achieved only incremental improvements when compared to the leading sequence-only approaches, highlighting unresolved challenges effectively leveraging these modalities together. Moreover, the function of certain proteins is highly dependent on the granular aspects of their surface topology, which have been overlooked by prior models. To address these limitations, we introduce the Sequence-Structure-Surface Fitness (S3F) model - a novel multimodal representation learning framework that integrates protein features across several scales. Our approach combines sequence representations from a protein language model with Geometric Vector Perceptron networks encoding protein backbone and detailed surface topology. The proposed method achieves state-of-the-art fitness prediction on the ProteinGym benchmark encompassing 217 substitution deep mutational scanning assays, and provides insights into the determinants of protein function. Our code is at https://github.com/DeepGraphLearning/S3F.

Dongxia Wu, Tsuyoshi Idé, Aurélie Lozano et al.

We address the problem of learning Granger causality from asynchronous, interdependent, multi-type event sequences. In particular, we are interested in discovering instance-level causal structures in an unsupervised manner. Instance-level causality identifies causal relationships among individual events, providing more fine-grained information for decision-making. Existing work in the literature either requires strong assumptions, such as linearity in the intensity function, or heuristically defined model parameters that do not necessarily meet the requirements of Granger causality. We propose Instance-wise Self-Attentive Hawkes Processes (ISAHP), a novel deep learning framework that can directly infer the Granger causality at the event instance level. ISAHP is the first neural point process model that meets the requirements of Granger causality. It leverages the self-attention mechanism of the transformer to align with the principles of Granger causality. We empirically demonstrate that ISAHP is capable of discovering complex instance-level causal structures that cannot be handled by classical models. We also show that ISAHP achieves state-of-the-art performance in proxy tasks involving type-level causal discovery and instance-level event type prediction.

Jiarui Lu, Xiaoyin Chen, Stephen Zhewen Lu et al.

Protein dynamics play a crucial role in protein biological functions and properties, and their traditional study typically relies on time-consuming molecular dynamics (MD) simulations conducted in silico. Recent advances in generative modeling, particularly denoising diffusion models, have enabled efficient accurate protein structure prediction and conformation sampling by learning distributions over crystallographic structures. However, effectively integrating physical supervision into these data-driven approaches remains challenging, as standard energy-based objectives often lead to intractable optimization. In this paper, we introduce Energy-based Alignment (EBA), a method that aligns generative models with feedback from physical models, efficiently calibrating them to appropriately balance conformational states based on their energy differences. Experimental results on the MD ensemble benchmark demonstrate that EBA achieves state-of-the-art performance in generating high-quality protein ensembles. By improving the physical plausibility of generated structures, our approach enhances model predictions and holds promise for applications in structural biology and drug discovery.

Amit Dhurandhar, Tejaswini Pedapati, Ronny Luss et al.

Transformer-based Language Models have become ubiquitous in Natural Language Processing (NLP) due to their impressive performance on various tasks. However, expensive training as well as inference remains a significant impediment to their widespread applicability. While enforcing sparsity at various levels of the model architecture has found promise in addressing scaling and efficiency issues, there remains a disconnect between how sparsity affects network topology. Inspired by brain neuronal networks, we explore sparsity approaches through the lens of network topology. Specifically, we exploit mechanisms seen in biological networks, such as preferential attachment and redundant synapse pruning, and show that principled, model-agnostic sparsity approaches are performant and efficient across diverse NLP tasks, spanning both classification (such as natural language inference) and generation (summarization, machine translation), despite our sole objective not being optimizing performance. NeuroPrune is competitive with (or sometimes superior to) baselines on performance and can be up to $10$x faster in terms of training time for a given level of sparsity, simultaneously exhibiting measurable improvements in inference time in many cases.

Payel Das, Ching-Yun Ko, Sihui Dai et al.

Large language models often expose their brittleness in reasoning tasks, especially while executing long chains of reasoning over context. We propose MemReasoner, a new and simple memory-augmented LLM architecture, in which the memory learns the relative order of facts in context, and enables hopping over them, while the decoder selectively attends to the memory. MemReasoner is trained end-to-end, with optional supporting fact supervision of varying degrees. We train MemReasoner, along with existing memory-augmented transformer models and a state-space model, on two distinct synthetic multi-hop reasoning tasks. Experiments performed under a variety of challenging scenarios, including the presence of long distractor text or target answer changes in test set, show strong generalization of MemReasoner on both single- and two-hop tasks. This generalization of MemReasoner is achieved using none-to-weak supporting fact supervision (using none and 1\% of supporting facts for one- and two-hop tasks, respectively). In contrast, baseline models overall struggle to generalize and benefit far less from using full supporting fact supervision. The results highlight the importance of explicit memory mechanisms, combined with additional weak supervision, for improving large language model's context processing ability toward reasoning tasks.

Zuobai Zhang, Jiarui Lu, Vijil Chenthamarakshan et al.

Protein function annotation is an important yet challenging task in biology. Recent deep learning advancements show significant potential for accurate function prediction by learning from protein sequences and structures. Nevertheless, these predictor-based methods often overlook the modeling of protein similarity, an idea commonly employed in traditional approaches using sequence or structure retrieval tools. To fill this gap, we first study the effect of inter-protein similarity modeling by benchmarking retriever-based methods against predictors on protein function annotation tasks. Our results show that retrievers can match or outperform predictors without large-scale pre-training. Building on these insights, we introduce a novel variational pseudo-likelihood framework, ProtIR, designed to improve function predictors by incorporating inter-protein similarity modeling. This framework iteratively refines knowledge between a function predictor and retriever, thereby combining the strengths of both predictors and retrievers. ProtIR showcases around 10% improvement over vanilla predictor-based methods. Besides, it achieves performance on par with protein language model-based methods, yet without the need for massive pre-training, highlighting the efficacy of our framework. Code will be released upon acceptance.

Georgios Kollias, Vasileios Kalantzis, Tsuyoshi Idé et al.

We introduce a new class of auto-encoders for directed graphs, motivated by a direct extension of the Weisfeiler-Leman algorithm to pairs of node labels. The proposed model learns pairs of interpretable latent representations for the nodes of directed graphs, and uses parameterized graph convolutional network (GCN) layers for its encoder and an asymmetric inner product decoder. Parameters in the encoder control the weighting of representations exchanged between neighboring nodes. We demonstrate the ability of the proposed model to learn meaningful latent embeddings and achieve superior performance on the directed link prediction task on several popular network datasets.

Igor Melnyk, Payel Das, Vijil Chenthamarakshan et al.

Computational protein design, i.e. inferring novel and diverse protein sequences consistent with a given structure, remains a major unsolved challenge. Recently, deep generative models that learn from sequences alone or from sequences and structures jointly have shown impressive performance on this task. However, those models appear limited in terms of modeling structural constraints, capturing enough sequence diversity, or both. Here we consider three recently proposed deep generative frameworks for protein design: (AR) the sequence-based autoregressive generative model, (GVP) the precise structure-based graph neural network, and Fold2Seq that leverages a fuzzy and scale-free representation of a three-dimensional fold, while enforcing structure-to-sequence (and vice versa) consistency. We benchmark these models on the task of computational design of antibody sequences, which demand designing sequences with high diversity for functional implication. The Fold2Seq framework outperforms the two other baselines in terms of diversity of the designed sequences, while maintaining the typical fold.

Jihun Yun, Aurelie C. Lozano, Eunho Yang

We study the training of regularized neural networks where the regularizer can be non-smooth and non-convex. We propose a unified framework for stochastic proximal gradient descent, which we term ProxGen, that allows for arbitrary positive preconditioners and lower semi-continuous regularizers. Our framework encompasses standard stochastic proximal gradient methods without preconditioners as special cases, which have been extensively studied in various settings. Not only that, we present two important update rules beyond the well-known standard methods as a byproduct of our approach: (i) the first closed-form proximal mappings of $\ell_q$ regularization ($0 \leq q \leq 1$) for adaptive stochastic gradient methods, and (ii) a revised version of ProxQuant that fixes a caveat of the original approach for quantization-specific regularizers. We analyze the convergence of ProxGen and show that the whole family of ProxGen enjoys the same convergence rate as stochastic proximal gradient descent without preconditioners. We also empirically show the superiority of proximal methods compared to subgradient-based approaches via extensive experiments. Interestingly, our results indicate that proximal methods with non-convex regularizers are more effective than those with convex regularizers.

Kyung-Su Kim, Aurélie C. Lozano, Eunho Yang

Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical learning theory. Especially, using the NTK-based approach, the following three representative results were obtained: (1) A training error bound was derived to show that networks can fit any finite training sample perfectly by reflecting a tighter characterization of training speed depending on the data complexity. (2) A generalization error bound invariant of network size was derived by using a data-dependent complexity measure (CMD). It follows from this CMD bound that networks can generalize arbitrary smooth functions. (3) A simple and analytic kernel function was derived as indeed equivalent to a fully-trained network. This kernel outperforms its corresponding network and the existing gold standard, Random Forests, in few shot learning. For all of these results to hold, the network scaling factor $κ$ should decrease w.r.t. sample size n. In this case of decreasing $κ$, however, we prove that the aforementioned results are surprisingly erroneous. It is because the output value of trained network decreases to zero when $κ$ decreases w.r.t. n. To solve this problem, we tighten key bounds by essentially removing $κ$-affected values. Our tighter analysis resolves the scaling problem and enables the validation of the original NTK-based results.

Jihun Yun, Aurelie C. Lozano, Eunho Yang

Adaptive gradient approaches that automatically adjust the learning rate on a per-feature basis have been very popular for training deep networks. This rich class of algorithms includes Adagrad, RMSprop, Adam, and recent extensions. All these algorithms have adopted diagonal matrix adaptation, due to the prohibitive computational burden of manipulating full matrices in high-dimensions. In this paper, we show that block-diagonal matrix adaptation can be a practical and powerful solution that can effectively utilize structural characteristics of deep learning architectures, and significantly improve convergence and out-of-sample generalization. We present a general framework with block-diagonal matrix updates via coordinate grouping, which includes counterparts of the aforementioned algorithms, prove their convergence in non-convex optimization, highlighting benefits compared to diagonal versions. In addition, we propose an efficient spectrum-clipping scheme that benefits from superior generalization performance of Sgd. Extensive experiments reveal that block-diagonal approaches achieve state-of-the-art results on several deep learning tasks, and can outperform adaptive diagonal methods, vanilla Sgd, as well as a modified version of full-matrix adaptation proposed very recently.

Tsui-Wei Weng, Huan Zhang, Pin-Yu Chen et al.

CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is an Extreme Value Theory (EVT) based robustness score for large-scale deep neural networks (DNNs). In this paper, we propose two extensions on this robustness score. First, we provide a new formal robustness guarantee for classifier functions that are twice differentiable. We apply extreme value theory on the new formal robustness guarantee and the estimated robustness is called second-order CLEVER score. Second, we discuss how to handle gradient masking, a common defensive technique, using CLEVER with Backward Pass Differentiable Approximation (BPDA). With BPDA applied, CLEVER can evaluate the intrinsic robustness of neural networks of a broader class -- networks with non-differentiable input transformations. We demonstrate the effectiveness of CLEVER with BPDA in experiments on a 121-layer Densenet model trained on the ImageNet dataset.

Ming Yu, Karthikeyan Natesan Ramamurthy, Addie Thompson et al.

We consider multi-response and multitask regression models, where the parameter matrix to be estimated is expected to have an unknown grouping structure. The groupings can be along tasks, or features, or both, the last one indicating a bi-cluster or "checkerboard" structure. Discovering this grouping structure along with parameter inference makes sense in several applications, such as multi-response Genome-Wide Association Studies. This additional structure can not only can be leveraged for more accurate parameter estimation, but it also provides valuable information on the underlying data mechanisms (e.g. relationships among genotypes and phenotypes in GWAS). In this paper, we propose two formulations to simultaneously learn the parameter matrix and its group structures, based on convex regularization penalties. We present optimization approaches to solve the resulting problems and provide numerical convergence guarantees. Our approaches are validated on extensive simulations and real datasets concerning phenotypes and genotypes of plant varieties.

Ming Yu, Addie M. Thompson, Karthikeyan Natesan Ramamurthy et al.

Inferring predictive maps between multiple input and multiple output variables or tasks has innumerable applications in data science. Multi-task learning attempts to learn the maps to several output tasks simultaneously with information sharing between them. We propose a novel multi-task learning framework for sparse linear regression, where a full task hierarchy is automatically inferred from the data, with the assumption that the task parameters follow a hierarchical tree structure. The leaves of the tree are the parameters for individual tasks, and the root is the global model that approximates all the tasks. We apply the proposed approach to develop and evaluate: (a) predictive models of plant traits using large-scale and automated remote sensing data, and (b) GWAS methodologies mapping such derived phenotypes in lieu of hand-measured traits. We demonstrate the superior performance of our approach compared to other methods, as well as the usefulness of discovering hierarchical groupings between tasks. Our results suggest that richer genetic mapping can indeed be obtained from the remote sensing data. In addition, our discovered groupings reveal interesting insights from a plant science perspective.

Meghana Kshirsagar, Eunho Yang, Aurélie C. Lozano

Sparse mapping has been a key methodology in many high-dimensional scientific problems. When multiple tasks share the set of relevant features, learning them jointly in a group drastically improves the quality of relevant feature selection. However, in practice this technique is used limitedly since such grouping information is usually hidden. In this paper, our goal is to recover the group structure on the sparsity patterns and leverage that information in the sparse learning. Toward this, we formulate a joint optimization problem in the task parameter and the group membership, by constructing an appropriate regularizer to encourage sparse learning as well as correct recovery of task groups. We further demonstrate that our proposed method recovers groups and the sparsity patterns in the task parameters accurately by extensive experiments.

Sahil Garg, Irina Rish, Guillermo Cecchi et al.

In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspired by the adult neurogenesis phenomenon in the dentate gyrus of the hippocampus, known to be associated with improved cognitive function and adaptation to new environments. In the online learning setting, where new input instances arrive sequentially in batches, the neuronal-birth is implemented by adding new units with random initial weights (random dictionary elements); the number of new units is determined by the current performance (representation error) of the dictionary, higher error causing an increase in the birth rate. Neuronal-death is implemented by imposing l1/l2-regularization (group sparsity) on the dictionary within the block-coordinate descent optimization at each iteration of our online alternating minimization scheme, which iterates between the code and dictionary updates. Finally, hidden unit connectivity adaptation is facilitated by introducing sparsity in dictionary elements. Our empirical evaluation on several real-life datasets (images and language) as well as on synthetic data demonstrates that the proposed approach can considerably outperform the state-of-art fixed-size (nonadaptive) online sparse coding of Mairal et al. (2009) in the presence of nonstationary data. Moreover, we identify certain properties of the data (e.g., sparse inputs with nearly non-overlapping supports) and of the model (e.g., dictionary sparsity) associated with such improvements.

A. Y. Aravkin, J. V. Burke, L. Ljung et al.

State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a convex quadratic objective function with structure induced by the dynamic model. These classical formulations fall short in many important circumstances. For instance, smoothers obtained using quadratic penalties can fail when outliers are present in the data, and cannot track impulsive inputs and abrupt state changes. Motivated by these shortcomings, generalized Kalman smoothing formulations have been proposed in the last few years, replacing quadratic models with more suitable, often nonsmooth, convex functions. In contrast to classical models, these general estimators require use of iterated algorithms, and these have received increased attention from control, signal processing, machine learning, and optimization communities. In this survey we show that the optimization viewpoint provides the control and signal processing community great freedom in the development of novel modeling and inference frameworks for dynamical systems. We discuss general statistical models for dynamic systems, making full use of nonsmooth convex penalties and constraints, and providing links to important models in signal processing and machine learning. We also survey optimization techniques for these formulations, paying close attention to dynamic problem structure. Modeling concepts and algorithms are illustrated with numerical examples.

Prasanna Sattigeri, Aurélie Lozano, Aleksandra Mojsilović et al.

Innovation is among the key factors driving a country's economic and social growth. But what are the factors that make a country innovative? How do they differ across different parts of the world and different stages of development? In this work done in collaboration with the World Economic Forum (WEF), we analyze the scores obtained through executive opinion surveys that constitute the WEF's Global Competitiveness Index in conjunction with other country-level metrics and indicators to identify actionable levers of innovation. The findings can help country leaders and organizations shape the policies to drive developmental activities and increase the capacity of innovation.

Eunho Yang, Aurelie Lozano, Aleksandr Aravkin

We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized M-estimators in the high-dimensional setting, including the popular Least Trimmed Squares estimator, as well as analogous estimators for generalized linear models and graphical models, using possibly non-convex loss functions. We present a general analysis of their statistical convergence rates and consistency, and then take a closer look at the trimmed versions of the Lasso and Graphical Lasso estimators as special cases. On the optimization side, we show how to extend algorithms for M-estimators to fit trimmed variants and provide guarantees on their numerical convergence. The generality and competitive performance of high-dimensional trimmed estimators are illustrated numerically on both simulated and real-world genomics data.

Jialei Wang, Peder A. Olsen, Andrew R. Conn et al.

We consider the problem of removing and replacing clouds in satellite image sequences, which has a wide range of applications in remote sensing. Our approach first detects and removes the cloud-contaminated part of the image sequences. It then recovers the missing scenes from the clean parts using the proposed "TECROMAC" (TEmporally Contiguous RObust MAtrix Completion) objective. The objective function balances temporal smoothness with a low rank solution while staying close to the original observations. The matrix whose the rows are pixels and columnsare days corresponding to the image, has low-rank because the pixels reflect land-types such as vegetation, roads and lakes and there are relatively few variations as a result. We provide efficient optimization algorithms for TECROMAC, so we can exploit images containing millions of pixels. Empirical results on real satellite image sequences, as well as simulated data, demonstrate that our approach is able to recover underlying images from heavily cloud-contaminated observations.

Eunho Yang, Aurélie C. Lozano

Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs. Our method guards against outliers by an implicit trimming mechanism akin to the popular Least Trimmed Squares method used for linear regression. We provide a rigorous statistical analysis of our estimator in the high-dimensional setting. In contrast, existing approaches for robust sparse GGMs estimation lack statistical guarantees. Our theoretical results are complemented by experiments on simulated and real gene expression data which further demonstrate the value of our approach.

Vikas Sindhwani, Ha Quang Minh, Aurelie Lozano

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function estimation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic developments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds.

Aleksandr Y. Aravkin, Anju Kambadur, Aurelie C. Lozano et al.

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the exploration of the entire conditional distribution of the response variable given the predictors and therefore yields a more comprehensive view of the important predictors. We propose a generalized OMP algorithm for variable selection, taking the misfit loss to be either the traditional quantile loss or a smooth version we call quantile Huber, and compare the resulting greedy approaches with convex sparsity-regularized formulations. We apply a recently proposed interior point methodology to efficiently solve all convex formulations as well as convex subproblems in the generalized OMP setting, pro- vide theoretical guarantees of consistent estimation, and demonstrate the performance of our approach using empirical studies of simulated and genomic datasets.

Aurélie C. Lozano, Nicolai Meinshausen

We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distance functionals, customarily used in nonparametric estimation for their robustness, with l1-regularization for high-dimensional regression. The geometry of MD-Lasso is key to its consistency and robustness. The estimator is governed by a scaling parameter that caps the influence of outliers: the loss per observation is locally convex and close to quadratic for small squared residuals, and flattens for squared residuals larger than the scaling parameter. As the parameter approaches infinity, the estimator becomes equivalent to least-squares Lasso. MD-Lasso enjoys fast convergence rates under mild conditions on the model error distribution, which hold for any of the solutions in a convexity region around the true parameter and in certain cases for every solution. Remarkably, a first-order optimization method is able to produce iterates very close to the consistent solutions, with geometric convergence and regardless of the initialization. A connection is established with re-weighted least-squares that intuitively explains MD-Lasso robustness. The merits of our method are demonstrated through simulation and eQTL data analysis.

Vikas Sindhwani, Minh Ha Quang, Aurelie C. Lozano

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function estimation problems, leading to novel nonlinear extensions of a class of Graphical Granger Causality techniques. Our algorithmic developments and extensive empirical studies are complemented by theoretical analyses in terms of Rademacher generalization bounds.