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This preliminary white paper proposes a novel 8-bit floating-point data format HiFloat8 (abbreviated as HiF8) for deep learning. HiF8 features tapered precision. For normal value encoding, it provides 7 exponent values with 3-bit mantissa, 8 exponent values with 2-bit mantissa, and 16 exponent values with 1-bit mantissa. For denormal value encoding, it extends the dynamic range by 7 extra powers of 2, from 31 to 38 binades (notice that FP16 covers 40 binades). Meanwhile, HiF8 encodes all the special values except that positive zero and negative zero are represented by only one bit-pattern. Thanks to the better balance between precision and dynamic range, HiF8 can be simultaneously used in both forward and backward passes of AI training. In this paper, we will describe the definition and rounding methods of HiF8, as well as the tentative training and inference solutions. To demonstrate the efficacy of HiF8, massive simulation results on various neural networks, including traditional neural networks and large language models (LLMs), will also be presented., Comment: 13 Pages, 4 Figures, 9 Tables

Recently, methods like Zero-1-2-3 have focused on single-view based 3D reconstruction and have achieved remarkable success. However, their predictions for unseen areas heavily rely on the inductive bias of large-scale pretrained diffusion models. Although subsequent work, such as DreamComposer, attempts to make predictions more controllable by incorporating additional views, the results remain unrealistic due to feature entanglement in the vanilla latent space, including factors such as lighting, material, and structure. To address these issues, we introduce the Visual Isotropy 3D Reconstruction Model (VI3DRM), a diffusion-based sparse views 3D reconstruction model that operates within an ID consistent and perspective-disentangled 3D latent space. By facilitating the disentanglement of semantic information, color, material properties and lighting, VI3DRM is capable of generating highly realistic images that are indistinguishable from real photographs. By leveraging both real and synthesized images, our approach enables the accurate construction of pointmaps, ultimately producing finely textured meshes or point clouds. On the NVS task, tested on the GSO dataset, VI3DRM significantly outperforms state-of-the-art method DreamComposer, achieving a PSNR of 38.61, an SSIM of 0.929, and an LPIPS of 0.027. Code will be made available upon publication.

The performance of anomaly inspection in industrial manufacturing is constrained by the scarcity of anomaly data. To overcome this challenge, researchers have started employing anomaly generation approaches to augment the anomaly dataset. However, existing anomaly generation methods suffer from limited diversity in the generated anomalies and struggle to achieve a seamless blending of this anomaly with the original image. In this paper, we overcome these challenges from a new perspective, simultaneously generating a pair of the overall image and the corresponding anomaly part. We propose DualAnoDiff, a novel diffusion-based few-shot anomaly image generation model, which can generate diverse and realistic anomaly images by using a dual-interrelated diffusion model, where one of them is employed to generate the whole image while the other one generates the anomaly part. Moreover, we extract background and shape information to mitigate the distortion and blurriness phenomenon in few-shot image generation. Extensive experiments demonstrate the superiority of our proposed model over state-of-the-art methods in terms of both realism and diversity. Overall, our approach significantly improves the performance of downstream anomaly detection tasks, including anomaly detection, anomaly localization, and anomaly classification tasks., Comment: Code: https://github.com/yinyjin/DualAnoDiff

Object detection in aerial images has always been a challenging task due to the generally small size of the objects. Most current detectors prioritize novel detection frameworks, often overlooking research on fundamental components such as feature pyramid networks. In this paper, we introduce the Cross-Layer Feature Pyramid Transformer (CFPT), a novel upsampler-free feature pyramid network designed specifically for small object detection in aerial images. CFPT incorporates two meticulously designed attention blocks with linear computational complexity: the Cross-Layer Channel-Wise Attention (CCA) and the Cross-Layer Spatial-Wise Attention (CSA). CCA achieves cross-layer interaction by dividing channel-wise token groups to perceive cross-layer global information along the spatial dimension, while CSA completes cross-layer interaction by dividing spatial-wise token groups to perceive cross-layer global information along the channel dimension. By integrating these modules, CFPT enables cross-layer interaction in one step, thereby avoiding the semantic gap and information loss associated with element-wise summation and layer-by-layer transmission. Furthermore, CFPT incorporates global contextual information, which enhances detection performance for small objects. To further enhance location awareness during cross-layer interaction, we propose the Cross-Layer Consistent Relative Positional Encoding (CCPE) based on inter-layer mutual receptive fields. We evaluate the effectiveness of CFPT on two challenging object detection datasets in aerial images, namely VisDrone2019-DET and TinyPerson. Extensive experiments demonstrate the effectiveness of CFPT, which outperforms state-of-the-art feature pyramid networks while incurring lower computational costs. The code will be released at https://github.com/duzw9311/CFPT.

Food is foundational to human life, serving not only as a source of nourishment but also as a cornerstone of cultural identity and social interaction. As the complexity of global dietary needs and preferences grows, food intelligence is needed to enable food perception and reasoning for various tasks, ranging from recipe generation and dietary recommendation to diet-disease correlation discovery and understanding. Towards this goal, for powerful capabilities across various domains and tasks in Large Language Models (LLMs), we introduce Food-oriented LLM FoodSky to comprehend food data through perception and reasoning. Considering the complexity and typicality of Chinese cuisine, we first construct one comprehensive Chinese food corpus FoodEarth from various authoritative sources, which can be leveraged by FoodSky to achieve deep understanding of food-related data. We then propose Topic-based Selective State Space Model (TS3M) and the Hierarchical Topic Retrieval Augmented Generation (HTRAG) mechanism to enhance FoodSky in capturing fine-grained food semantics and generating context-aware food-relevant text, respectively. Our extensive evaluations demonstrate that FoodSky significantly outperforms general-purpose LLMs in both chef and dietetic examinations, with an accuracy of 67.2% and 66.4% on the Chinese National Chef Exam and the National Dietetic Exam, respectively. FoodSky not only promises to enhance culinary creativity and promote healthier eating patterns, but also sets a new standard for domain-specific LLMs that address complex real-world issues in the food domain. An online demonstration of FoodSky is available at http://222.92.101.211:8200., Comment: 32 pages, 19 figures

Ranking algorithms are fundamental to various online platforms across e-commerce sites to content streaming services. Our research addresses the challenge of adaptively ranking items from a candidate pool for heterogeneous users, a key component in personalizing user experience. We develop a user response model that considers diverse user preferences and the varying effects of item positions, aiming to optimize overall user satisfaction with the ranked list. We frame this problem within a contextual bandits framework, with each ranked list as an action. Our approach incorporates an upper confidence bound to adjust predicted user satisfaction scores and selects the ranking action that maximizes these adjusted scores, efficiently solved via maximum weight imperfect matching. We demonstrate that our algorithm achieves a cumulative regret bound of $O(d\sqrt{NKT})$ for ranking $K$ out of $N$ items in a $d$-dimensional context space over $T$ rounds, under the assumption that user responses follow a generalized linear model. This regret alleviates dependence on the ambient action space, whose cardinality grows exponentially with $N$ and $K$ (thus rendering direct application of existing adaptive learning algorithms -- such as UCB or Thompson sampling -- infeasible). Experiments conducted on both simulated and real-world datasets demonstrate our algorithm outperforms the baseline., Comment: 25 pages in total. Includes 4 figures and a pdf. International conference on machine learning. PMLR, 2024

Predicting the timing and occurrence of events is a major focus of data science applications, especially in the context of biomedical research. Performance for models estimating these outcomes, often referred to as time-to-event or survival outcomes, is frequently summarized using measures of discrimination, in particular time-dependent AUC and concordance. Many estimators for these quantities have been proposed which can be broadly categorized as either semi-parametric estimators or non-parametric estimators. In this paper, we review various estimators' mathematical construction and compare the behavior of the two classes of estimators. Importantly, we identify a previously unknown feature of the class of semi-parametric estimators that can result in vastly over-optimistic out-of-sample estimation of discriminative performance in common applied tasks. Although these semi-parametric estimators are popular in practice, the phenomenon we identify here suggests this class of estimators may be inappropriate for use in model assessment and selection based on out-of-sample evaluation criteria. This is due to the semi-parametric estimators' bias in favor of models that are overfit when using out-of-sample prediction criteria (e.g., cross validation). Non-parametric estimators, which do not exhibit this behavior, are highly variable for local discrimination. We propose to address the high variability problem through penalized regression splines smoothing. The behavior of various estimators of time-dependent AUC and concordance are illustrated via a simulation study using two different mechanisms that produce over-optimistic out-of-sample estimates using semi-parametric estimators. Estimators are further compared using a case study using data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014.

Instruction-based image editing focuses on equipping a generative model with the capacity to adhere to human-written instructions for editing images. Current approaches typically comprehend explicit and specific instructions. However, they often exhibit a deficiency in executing active reasoning capacities required to comprehend instructions that are implicit or insufficiently defined. To enhance active reasoning capabilities and impart intelligence to the editing model, we introduce ReasonPix2Pix, a comprehensive reasoning-attentive instruction editing dataset. The dataset is characterized by 1) reasoning instruction, 2) more realistic images from fine-grained categories, and 3) increased variances between input and edited images. When fine-tuned with our dataset under supervised conditions, the model demonstrates superior performance in instructional editing tasks, independent of whether the tasks require reasoning or not. The code will be available at https://github.com/Jin-Ying/ReasonPix2Pix.

Before deploying outputs from foundation models in high-stakes tasks, it is imperative to ensure that they align with human values. For instance, in radiology report generation, reports generated by a vision-language model must align with human evaluations before their use in medical decision-making. This paper presents Conformal Alignment, a general framework for identifying units whose outputs meet a user-specified alignment criterion. It is guaranteed that on average, a prescribed fraction of selected units indeed meet the alignment criterion, regardless of the foundation model or the data distribution. Given any pre-trained model and new units with model-generated outputs, Conformal Alignment leverages a set of reference data with ground-truth alignment status to train an alignment predictor. It then selects new units whose predicted alignment scores surpass a data-dependent threshold, certifying their corresponding outputs as trustworthy. Through applications to question answering and radiology report generation, we demonstrate that our method is able to accurately identify units with trustworthy outputs via lightweight training over a moderate amount of reference data. En route, we investigate the informativeness of various features in alignment prediction and combine them with standard models to construct the alignment predictor.

Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn new test point with a prescribed probability. However, a common scenario in practice is that, after seeing the data, practitioners decide which test unit(s) to focus on in a data-driven manner and seek for uncertainty quantification of the focal unit(s). In such cases, marginally valid conformal prediction intervals may not provide valid coverage for the focal unit(s) due to selection bias. This paper presents a general framework for constructing a prediction set with finite-sample exact coverage conditional on the unit being selected by a given procedure. The general form of our method works for arbitrary selection rules that are invariant to the permutation of the calibration units, and generalizes Mondrian Conformal Prediction to multiple test units and non-equivariant classifiers. We then work out the computationally efficient implementation of our framework for a number of realistic selection rules, including top-K selection, optimization-based selection, selection based on conformal p-values, and selection based on properties of preliminary conformal prediction sets. The performance of our methods is demonstrated via applications in drug discovery and health risk prediction.

We consider multi-source free domain adaptation, the problem of adapting multiple existing models to a new domain without accessing the source data. Among existing approaches, methods based on model ensemble are effective in both the source and target domains, but incur significantly increased computational costs. Towards this dilemma, in this work, we propose a novel framework called SepRep-Net, which tackles multi-source free domain adaptation via model Separation and Reparameterization.Concretely, SepRep-Net reassembled multiple existing models to a unified network, while maintaining separate pathways (Separation). During training, separate pathways are optimized in parallel with the information exchange regularly performed via an additional feature merging unit. With our specific design, these pathways can be further reparameterized into a single one to facilitate inference (Reparameterization). SepRep-Net is characterized by 1) effectiveness: competitive performance on the target domain, 2) efficiency: low computational costs, and 3) generalizability: maintaining more source knowledge than existing solutions. As a general approach, SepRep-Net can be seamlessly plugged into various methods. Extensive experiments validate the performance of SepRep-Net on mainstream benchmarks.

Global food systems confront the urgent challenge of supplying sustainable, nutritious diets in the face of escalating demands. The advent of Artificial Intelligence (AI) is bringing in a personal choice revolution, wherein AI-driven individual decisions transform food systems from dinner tables, to the farms, and back to our plates. In this context, AI algorithms refine personal dietary choices, subsequently shaping agricultural outputs, and promoting an optimized feedback loop from consumption to cultivation. Initially, we delve into AI tools and techniques spanning the food supply chain, and subsequently assess how AI subfields$\unicode{x2013}$encompassing machine learning, computer vision, and speech recognition$\unicode{x2013}$are harnessed within the AI-enabled Food System (AIFS) framework, which increasingly leverages Internet of Things, multimodal sensors and real-time data exchange. We spotlight the AIFS framework, emphasizing its fusion of AI with technologies such as digitalization, big data analytics, biotechnology, and IoT extensively used in modern food systems in every component. This paradigm shifts the conventional "farm to fork" narrative to a cyclical "consumer-driven farm to fork" model for better achieving sustainable, nutritious diets. This paper explores AI's promise and the intrinsic challenges it poses within the food domain. By championing stringent AI governance, uniform data architectures, and cross-disciplinary partnerships, we argue that AI, when synergized with consumer-centric strategies, holds the potential to steer food systems toward a sustainable trajectory. We furnish a comprehensive survey for the state-of-the-art in diverse facets of food systems, subsequently pinpointing gaps and advocating for the judicious and efficacious deployment of emergent AI methodologies.

Unsupervised domain adaptation (UDA) is a pivotal form in machine learning to extend the in-domain model to the distinctive target domains where the data distributions differ. Most prior works focus on capturing the inter-domain transferability but largely overlook rich intra-domain structures, which empirically results in even worse discriminability. In this work, we introduce a novel graph SPectral Alignment (SPA) framework to tackle the tradeoff. The core of our method is briefly condensed as follows: (i)-by casting the DA problem to graph primitives, SPA composes a coarse graph alignment mechanism with a novel spectral regularizer towards aligning the domain graphs in eigenspaces; (ii)-we further develop a fine-grained message propagation module -- upon a novel neighbor-aware self-training mechanism -- in order for enhanced discriminability in the target domain. On standardized benchmarks, the extensive experiments of SPA demonstrate that its performance has surpassed the existing cutting-edge DA methods. Coupled with dense model analysis, we conclude that our approach indeed possesses superior efficacy, robustness, discriminability, and transferability. Code and data are available at: https://github.com/CrownX/SPA., Comment: NeurIPS 2023 camera ready

Food detection is becoming a fundamental task in food computing that supports various multimedia applications, including food recommendation and dietary monitoring. To deal with real-world scenarios, food detection needs to localize and recognize novel food objects that are not seen during training, demanding Zero-Shot Detection (ZSD). However, the complexity of semantic attributes and intra-class feature diversity poses challenges for ZSD methods in distinguishing fine-grained food classes. To tackle this, we propose the Semantic Separable Diffusion Synthesizer (SeeDS) framework for Zero-Shot Food Detection (ZSFD). SeeDS consists of two modules: a Semantic Separable Synthesizing Module (S$^3$M) and a Region Feature Denoising Diffusion Model (RFDDM). The S$^3$M learns the disentangled semantic representation for complex food attributes from ingredients and cuisines, and synthesizes discriminative food features via enhanced semantic information. The RFDDM utilizes a novel diffusion model to generate diversified region features and enhances ZSFD via fine-grained synthesized features. Extensive experiments show the state-of-the-art ZSFD performance of our proposed method on two food datasets, ZSFooD and UECFOOD-256. Moreover, SeeDS also maintains effectiveness on general ZSD datasets, PASCAL VOC and MS COCO. The code and dataset can be found at https://github.com/LanceZPF/SeeDS., Comment: Accepted by ACM Multimedia 2023

Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental contexts, then studies conducted in different populations will estimate different average effects. This paper uses ``generalizability" methods to quantify how much of the effect size discrepancy between an original study and its replication can be explained by distribution shift on observed unit-level characteristics. More specifically, we decompose this discrepancy into ``components" attributable to sampling variability (including publication bias), observable distribution shifts, and residual factors. We compute this decomposition for several directly-replicated behavioral science experiments and find little evidence that observable distribution shifts contribute appreciably to non-replicability. In some cases, this is because there is too much statistical noise. In other cases, there is strong evidence that controlling for additional moderators is necessary for reliable replication.

This paper introduces novel weighted conformal p-values and methods for model-free selective inference. The problem is as follows: given test units with covariates $X$ and missing responses $Y$, how do we select units for which the responses $Y$ are larger than user-specified values while controlling the proportion of false positives? Can we achieve this without any modeling assumptions on the data and without any restriction on the model for predicting the responses? Last, methods should be applicable when there is a covariate shift between training and test data, which commonly occurs in practice. We answer these questions by first leveraging any prediction model to produce a class of well-calibrated weighted conformal p-values, which control the type-I error in detecting a large response. These p-values cannot be passed on to classical multiple testing procedures since they may not obey a well-known positive dependence property. Hence, we introduce weighted conformalized selection (WCS), a new procedure which controls false discovery rate (FDR) in finite samples. Besides prediction-assisted candidate selection, WCS (1) allows to infer multiple individual treatment effects, and (2) extends to outlier detection with inlier distributions shifts. We demonstrate performance via simulations and applications to causal inference, drug discovery, and outlier detection datasets.

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features., Comment: Published at NeurIPS 2023

Interpreting natural language is an increasingly important task in computer algorithms due to the growing availability of unstructured textual data. Natural Language Processing (NLP) applications rely on semantic networks for structured knowledge representation. The fundamental properties of semantic networks must be taken into account when designing NLP algorithms, yet they remain to be structurally investigated. We study the properties of semantic networks from ConceptNet, defined by 7 semantic relations from 11 different languages. We find that semantic networks have universal basic properties: they are sparse, highly clustered, and many exhibit power-law degree distributions. Our findings show that the majority of the considered networks are scale-free. Some networks exhibit language-specific properties determined by grammatical rules, for example networks from highly inflected languages, such as e.g. Latin, German, French and Spanish, show peaks in the degree distribution that deviate from a power law. We find that depending on the semantic relation type and the language, the link formation in semantic networks is guided by different principles. In some networks the connections are similarity-based, while in others the connections are more complementarity-based. Finally, we demonstrate how knowledge of similarity and complementarity in semantic networks can improve NLP algorithms in missing link inference.

In this paper, we consider the continuity of the inverse in (strongly) paratopological gyrogroups. The conclusions are established as follows: (1) A compact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2) A Hausdorff locally compact strongly paratopological gyrogroup is a topological gyrogroup. (3) If $G$ is locally compact strongly paratopological gyrocommutative gyrogroup (without any separation restrictions), then $G$ is a strongly topological gyrogroup. (4) Every regular feebly compact strongly paratopological gyrogroup is a topological gyrogroup. (5) If a Hausdorff strongly paratopological gyrogroup $G$ is countablly compact and topologically periodic, then $G$ is a strongly topological gyrogroup.

Real-world data contains a vast amount of multimodal information, among which vision and language are the two most representative modalities. Moreover, increasingly heavier models, \textit{e}.\textit{g}., Transformers, have attracted the attention of researchers to model compression. However, how to compress multimodal models, especially vison-language Transformers, is still under-explored. This paper proposes the \textbf{U}nified and \textbf{P}r\textbf{o}gressive \textbf{P}runing (\textbf{\emph{UPop}}) as a universal vison-language Transformer compression framework, which incorporates 1) unifiedly searching multimodal subnets in a continuous optimization space from the original model, which enables automatic assignment of pruning ratios among compressible modalities and structures; 2) progressively searching and retraining the subnet, which maintains convergence between the search and retrain to attain higher compression ratios. Experiments on various tasks, datasets, and model architectures demonstrate the effectiveness and versatility of the proposed UPop framework. The code is available at https://github.com/sdc17/UPop., Comment: ICML 2023. Website: https://dachuanshi.com/UPop-Project

Semi-Supervised Semantic Segmentation aims at training the segmentation model with limited labeled data and a large amount of unlabeled data. To effectively leverage the unlabeled data, pseudo labeling, along with the teacher-student framework, is widely adopted in semi-supervised semantic segmentation. Though proved to be effective, this paradigm suffers from incorrect pseudo labels which inevitably exist and are taken as auxiliary training data. To alleviate the negative impact of incorrect pseudo labels, we delve into the current Semi-Supervised Semantic Segmentation frameworks. We argue that the unlabeled data with pseudo labels can facilitate the learning of representative features in the feature extractor, but it is unreliable to supervise the mask predictor. Motivated by this consideration, we propose a novel framework, Gentle Teaching Assistant (GTA-Seg) to disentangle the effects of pseudo labels on feature extractor and mask predictor of the student model. Specifically, in addition to the original teacher-student framework, our method introduces a teaching assistant network which directly learns from pseudo labels generated by the teacher network. The gentle teaching assistant (GTA) is coined gentle since it only transfers the beneficial feature representation knowledge in the feature extractor to the student model in an Exponential Moving Average (EMA) manner, protecting the student model from the negative influences caused by unreliable pseudo labels in the mask predictor. The student model is also supervised by reliable labeled data to train an accurate mask predictor, further facilitating feature representation. Extensive experiment results on benchmark datasets validate that our method shows competitive performance against previous methods. Code is available at https://github.com/Jin-Ying/GTA-Seg., Comment: NeurIPS2022 camera ready

This paper studies offline policy learning, which aims at utilizing observations collected a priori (from either fixed or adaptively evolving behavior policies) to learn an optimal individualized decision rule that achieves the best overall outcomes for a given population. Existing policy learning methods rely on a uniform overlap assumption, i.e., the propensities of exploring all actions for all individual characteristics must be lower bounded. As one has no control over the data collection process, this assumption can be unrealistic in many situations, especially when the behavior policies are allowed to evolve over time with diminishing propensities for certain actions. In this paper, we propose Pessimistic Policy Learning (PPL), a new algorithm that optimizes lower confidence bounds (LCBs) -- instead of point estimates -- of the policy values. The LCBs are constructed using knowledge of the behavior policies for collecting the offline data. Without assuming any uniform overlap condition, we establish a data-dependent upper bound for the suboptimality of our algorithm, which only depends on (i) the overlap for the optimal policy, and (ii) the complexity of the policy class we optimize over. As an implication, for adaptively collected data, we ensure efficient policy learning as long as the propensities for optimal actions are lower bounded over time, while those for suboptimal ones are allowed to diminish arbitrarily fast. In our theoretical analysis, we develop a new self-normalized type concentration inequality for inverse-propensity-weighting estimators, generalizing the well-known empirical Bernstein's inequality to unbounded and non-i.i.d. data. We complement our theory with an efficient optimization algorithm via Majorization-Minimization and policy tree search, as well as extensive simulation studies and real-world applications that demonstrate the efficacy of PPL.

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our method follows the routine: (i) decomposing the regression task into several sub-tasks, (ii) fitting the sub-task models, and (iii) using the sub-task models to provide an improved estimate for the original regression problem. This routine applies to widely-used low-dimensional (generalized) linear models and high-dimensional regularized linear regression. It also naturally extends to missing-data settings where only partial observations are available. By incorporating auxiliary information, our approach improves the estimation efficiency and prediction accuracy upon linear regression or the Lasso under a conditional independence assumption for predicting the outcome. For high-dimensional settings, we develop an extension of our procedure that is robust to violations of the conditional independence assumption, in the sense that it improves efficiency if this assumption holds and coincides with the Lasso otherwise. We demonstrate the efficacy of our methods with simulated and real data sets., Comment: Journal of Machine Learning Research