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Rule-based neural networks stand out for enabling interpretable classification by learning logical rules for both prediction and interpretation. However, existing models often lack flexibility due to the fixed model structure. Addressing this, we introduce the Normal Form Rule Learner (NFRL) algorithm, leveraging a selective discrete neural network, that treat weight parameters as hard selectors, to learn rules in both Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF) for enhanced accuracy and interpretability. Instead of adopting a deep, complex structure, the NFRL incorporates two specialized Normal Form Layers (NFLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Normal Form Constraint (NFC) to streamline neuron connections. We also show the novel network architecture can be optimized using adaptive gradient update together with Straight-Through Estimator to overcome the gradient vanishing challenge. Through extensive experiments on 11 datasets, NFRL demonstrates superior classification performance, quality of learned rules, efficiency and interpretability compared to 12 state-of-the-art alternatives. Code and data are available at \url{https://anonymous.4open.science/r/NFRL-27B4/}., Comment: 19 pages, 62 figures

In this work, we present a comprehensive three-phase study to examine (1) the effectiveness of large multimodal models (LMMs) in recognizing cultural contexts; (2) the accuracy of their representations of diverse cultures; and (3) their ability to adapt content across cultural boundaries. We first introduce Dalle Street, a large-scale dataset generated by DALL-E 3 and validated by humans, containing 9,935 images of 67 countries and 10 concept classes. We reveal disparities in cultural understanding at the sub-region level with both open-weight (LLaVA) and closed-source (GPT-4V) models on Dalle Street and other existing benchmarks. Next, we assess models' deeper culture understanding by an artifact extraction task and identify over 18,000 artifacts associated with different countries. Finally, we propose a highly composable pipeline, CultureAdapt, to adapt images from culture to culture. Our findings reveal a nuanced picture of the cultural competence of LMMs, highlighting the need to develop culture-aware systems. Dataset and code are available at https://github.com/iamshnoo/crossroads, Comment: under review

Existing works examining Vision Language Models (VLMs) for social biases predominantly focus on a limited set of documented bias associations, such as gender:profession or race:crime. This narrow scope often overlooks a vast range of unexamined implicit associations, restricting the identification and, hence, mitigation of such biases. We address this gap by probing VLMs to (1) uncover hidden, implicit associations across 9 bias dimensions. We systematically explore diverse input and output modalities and (2) demonstrate how biased associations vary in their negativity, toxicity, and extremity. Our work (3) identifies subtle and extreme biases that are typically not recognized by existing methodologies. We make the Dataset of retrieved associations, (Dora), publicly available here https://github.com/chahatraj/BiasDora., Comment: Under Review

Large Language Models (LLMs) perpetuate social biases, reflecting prejudices in their training data and reinforcing societal stereotypes and inequalities. Our work explores the potential of the Contact Hypothesis, a concept from social psychology for debiasing LLMs. We simulate various forms of social contact through LLM prompting to measure their influence on the model's biases, mirroring how intergroup interactions can reduce prejudices in social contexts. We create a dataset of 108,000 prompts following a principled approach replicating social contact to measure biases in three LLMs (LLaMA 2, Tulu, and NousHermes) across 13 social bias dimensions. We propose a unique debiasing technique, Social Contact Debiasing (SCD), that instruction-tunes these models with unbiased responses to prompts. Our research demonstrates that LLM responses exhibit social biases when subject to contact probing, but more importantly, these biases can be significantly reduced by up to 40% in 1 epoch of instruction tuning LLaMA 2 following our SCD strategy. Our code and data are available at https://github.com/chahatraj/breakingbias., Comment: Under Review

Collaborative filtering (CF) based recommendations suffer from mainstream bias -- where mainstream users are favored over niche users, leading to poor recommendation quality for many long-tail users. In this paper, we identify two root causes of this mainstream bias: (i) discrepancy modeling, whereby CF algorithms focus on modeling mainstream users while neglecting niche users with unique preferences; and (ii) unsynchronized learning, where niche users require more training epochs than mainstream users to reach peak performance. Targeting these causes, we propose a novel end-To-end Adaptive Local Learning (TALL) framework to provide high-quality recommendations to both mainstream and niche users. TALL uses a loss-driven Mixture-of-Experts module to adaptively ensemble experts to provide customized local models for different users. Further, it contains an adaptive weight module to synchronize the learning paces of different users by dynamically adjusting weights in the loss. Extensive experiments demonstrate the state-of-the-art performance of the proposed model. Code and data are provided at \url{https://github.com/JP-25/end-To-end-Adaptive-Local-Leanring-TALL-}, Comment: ECIR 2024

Machine Unlearning (MU) algorithms have become increasingly critical due to the imperative adherence to data privacy regulations. The primary objective of MU is to erase the influence of specific data samples on a given model without the need to retrain it from scratch. Accordingly, existing methods focus on maximizing user privacy protection. However, there are different degrees of privacy regulations for each real-world web-based application. Exploring the full spectrum of trade-offs between privacy, model utility, and runtime efficiency is critical for practical unlearning scenarios. Furthermore, designing the MU algorithm with simple control of the aforementioned trade-off is desirable but challenging due to the inherent complex interaction. To address the challenges, we present Controllable Machine Unlearning (ConMU), a novel framework designed to facilitate the calibration of MU. The ConMU framework contains three integral modules: an important data selection module that reconciles the runtime efficiency and model generalization, a progressive Gaussian mechanism module that balances privacy and model generalization, and an unlearning proxy that controls the trade-offs between privacy and runtime efficiency. Comprehensive experiments on various benchmark datasets have demonstrated the robust adaptability of our control mechanism and its superiority over established unlearning methods. ConMU explores the full spectrum of the Privacy-Utility-Efficiency trade-off and allows practitioners to account for different real-world regulations. Source code available at: https://github.com/guangyaodou/ConMU., Comment: Accepted by The Web Conference (WWW) 2024

Human biases are ubiquitous but not uniform: disparities exist across linguistic, cultural, and societal borders. As large amounts of recent literature suggest, language models (LMs) trained on human data can reflect and often amplify the effects of these social biases. However, the vast majority of existing studies on bias are heavily skewed towards Western and European languages. In this work, we scale the Word Embedding Association Test (WEAT) to 24 languages, enabling broader studies and yielding interesting findings about LM bias. We additionally enhance this data with culturally relevant information for each language, capturing local contexts on a global scale. Further, to encompass more widely prevalent societal biases, we examine new bias dimensions across toxicity, ableism, and more. Moreover, we delve deeper into the Indian linguistic landscape, conducting a comprehensive regional bias analysis across six prevalent Indian languages. Finally, we highlight the significance of these social biases and the new dimensions through an extensive comparison of embedding methods, reinforcing the need to address them in pursuit of more equitable language models. All code, data and results are available here: https://github.com/iamshnoo/weathub., Comment: accepted at EMNLP 2023

Pre-trained Language Models are widely used in many important real-world applications. However, recent studies show that these models can encode social biases from large pre-training corpora and even amplify biases in downstream applications. To address this challenge, we propose Co$^2$PT, an efficient and effective debias-while-prompt tuning method for mitigating biases via counterfactual contrastive prompt tuning on downstream tasks. Our experiments conducted on three extrinsic bias benchmarks demonstrate the effectiveness of Co$^2$PT on bias mitigation during the prompt tuning process and its adaptability to existing upstream debiased language models. These findings indicate the strength of Co$^2$PT and provide promising avenues for further enhancement in bias mitigation on downstream tasks., Comment: To appear in Findings of EMNLP 2023

Question generation is a widely used data augmentation approach with extensive applications, and extracting qualified candidate answers from context passages is a critical step for most question generation systems. However, existing methods for candidate answer extraction are reliant on linguistic rules or annotated data that face the partial annotation issue and challenges in generalization. To overcome these limitations, we propose a novel unsupervised candidate answer extraction approach that leverages the inherent structure of context passages through a Differentiable Masker-Reconstructor (DMR) Model with the enforcement of self-consistency for picking up salient information tokens. We curated two datasets with exhaustively-annotated answers and benchmark a comprehensive set of supervised and unsupervised candidate answer extraction methods. We demonstrate the effectiveness of the DMR model by showing its performance is superior among unsupervised methods and comparable to supervised methods., Comment: EMNLP 2023 - Findings

Spoken languages show significant variation across mandarin and accent. Despite the high performance of mandarin automatic speech recognition (ASR), accent ASR is still a challenge task. In this paper, we introduce meta-learning techniques for fast accent domain expansion in mandarin speech recognition, which expands the field of accents without deteriorating the performance of mandarin ASR. Meta-learning or learn-to-learn can learn general relation in multi domains not only for over-fitting a specific domain. So we select meta-learning in the domain expansion task. This more essential learning will cause improved performance on accent domain extension tasks. We combine the methods of meta learning and freeze of model parameters, which makes the recognition performance more stable in different cases and the training faster about 20%. Our approach significantly outperforms other methods about 3% relatively in the accent domain expansion task. Compared to the baseline model, it improves relatively 37% under the condition that the mandarin test set remains unchanged. In addition, it also proved this method to be effective on a large amount of data with a relative performance improvement of 4% on the accent test set.

A key component of modern conversational systems is the Dialogue State Tracker (or DST), which models a user's goals and needs. Toward building more robust and reliable DSTs, we introduce a prompt-based learning approach to automatically generate effective adversarial examples to probe DST models. Two key characteristics of this approach are: (i) it only needs the output of the DST with no need for model parameters, and (ii) it can learn to generate natural language utterances that can target any DST. Through experiments over state-of-the-art DSTs, the proposed framework leads to the greatest reduction in accuracy and the best attack success rate while maintaining good fluency and a low perturbation ratio. We also show how much the generated adversarial examples can bolster a DST through adversarial training. These results indicate the strength of prompt-based attacks on DSTs and leave open avenues for continued refinement., Comment: To appear in Findings of ACL 2023

We present a fully differentiable framework for seamlessly integrating wave optical components with geometrical lenses, offering an approach to enhance the performance of large-scale end-to-end optical systems. In this study, we focus on the integration of a metalens, a geometrical lens, and image data. Through the use of gradient-based optimization techniques, we demonstrate the design of nonparaxial imaging systems and the correction of aberrations inherent in geometrical optics. Our framework enables efficient and effective optimization of the entire optical system, leading to improved overall performance., Comment: 14 pages, 10 figures

Conversational recommenders are emerging as a powerful tool to personalize a user's recommendation experience. Through a back-and-forth dialogue, users can quickly hone in on just the right items. Many approaches to conversational recommendation, however, only partially explore the user preference space and make limiting assumptions about how user feedback can be best incorporated, resulting in long dialogues and poor recommendation performance. In this paper, we propose a novel conversational recommendation framework with two unique features: (i) a greedy NDCG attribute selector, to enhance user personalization in the interactive preference elicitation process by prioritizing attributes that most effectively represent the actual preference space of the user; and (ii) a user representation refiner, to effectively fuse together the user preferences collected from the interactive elicitation process to obtain a more personalized understanding of the user. Through extensive experiments on four frequently used datasets, we find the proposed framework not only outperforms all the state-of-the-art conversational recommenders (in terms of both recommendation performance and conversation efficiency), but also provides a more personalized experience for the user under the proposed multi-groundtruth multi-round conversational recommendation setting., Comment: To Appear On TheWebConf (WWW) 2023

Recent work in news recommendation has demonstrated that recommenders can over-expose users to articles that support their pre-existing opinions. However, most existing work focuses on a static setting or over a short-time window, leaving open questions about the long-term and dynamic impacts of news recommendations. In this paper, we explore these dynamic impacts through a systematic study of three research questions: 1) How do the news reading behaviors of users change after repeated long-term interactions with recommenders? 2) How do the inherent preferences of users change over time in such a dynamic recommender system? 3) Can the existing SOTA static method alleviate the problem in the dynamic environment? Concretely, we conduct a comprehensive data-driven study through simulation experiments of political polarization in news recommendations based on 40,000 annotated news articles. We find that users are rapidly exposed to more extreme content as the recommender evolves. We also find that a calibration-based intervention can slow down this polarization, but leaves open significant opportunities for future improvements

For decades, best subset selection (BSS) has eluded statisticians mainly due to its computational bottleneck. However, until recently, modern computational breakthroughs have rekindled theoretical interest in BSS and have led to new findings. Recently, \cite{guo2020best} showed that the model selection performance of BSS is governed by a margin quantity that is robust to the design dependence, unlike modern methods such as LASSO, SCAD, MCP, etc. Motivated by their theoretical results, in this paper, we also study the variable selection properties of best subset selection for high-dimensional sparse linear regression setup. We show that apart from the identifiability margin, the following two complexity measures play a fundamental role in characterizing the margin condition for model consistency: (a) complexity of \emph{residualized features}, (b) complexity of \emph{spurious projections}. In particular, we establish a simple margin condition that depends only on the identifiability margin and the dominating one of the two complexity measures. Furthermore, we show that a margin condition depending on similar margin quantity and complexity measures is also necessary for model consistency of BSS. For a broader understanding, we also consider some simple illustrative examples to demonstrate the variation in the complexity measures that refines our theoretical understanding of the model selection performance of BSS under different correlation structures., Comment: 46 pages, 2 Figures

Conversational recommender systems have demonstrated great success. They can accurately capture a user's current detailed preference -- through a multi-round interaction cycle -- to effectively guide users to a more personalized recommendation. Alas, conversational recommender systems can be plagued by the adverse effects of bias, much like traditional recommenders. In this work, we argue for increased attention on the presence of and methods for counteracting bias in these emerging systems. As a starting point, we propose three fundamental questions that should be deeply examined to enable fairness in conversational recommender systems., Comment: arXiv admin note: substantial text overlap with arXiv:2208.03298

Conversational recommender systems (CRS) have shown great success in accurately capturing a user's current and detailed preference through the multi-round interaction cycle while effectively guiding users to a more personalized recommendation. Perhaps surprisingly, conversational recommender systems can be plagued by popularity bias, much like traditional recommender systems. In this paper, we systematically study the problem of popularity bias in CRSs. We demonstrate the existence of popularity bias in existing state-of-the-art CRSs from an exposure rate, a success rate, and a conversational utility perspective, and propose a suite of popularity bias metrics designed specifically for the CRS setting. We then introduce a debiasing framework with three unique features: (i) Popularity-Aware Focused Learning to reduce the popularity-distorting impact on preference prediction; (ii) Cold-Start Item Embedding Reconstruction via Attribute Mapping, to improve the modeling of cold-start items; and (iii) Dual-Policy Learning, to better guide the CRS when dealing with either popular or unpopular items. Through extensive experiments on two frequently used CRS datasets, we find the proposed model-agnostic debiasing framework not only mitigates the popularity bias in state-of-the-art CRSs but also improves the overall recommendation performance., Comment: to appear in CIKM22

In this paper, we propose a one-shot distributed learning algorithm via refitting bootstrap samples, which we refer to as ReBoot. ReBoot refits a new model to mini-batches of bootstrap samples that are continuously drawn from each of the locally fitted models. It requires only one round of communication of model parameters without much memory. Theoretically, we analyze the statistical error rate of ReBoot for generalized linear models (GLM) and noisy phase retrieval, which represent convex and non-convex problems, respectively. In both cases, ReBoot provably achieves the full-sample statistical rate. In particular, we show that the systematic bias of ReBoot, the error that is independent of the number of subsamples (i.e., the number of sites), is $O(n ^ {-2})$ in GLM, where $n$ is the subsample size (the sample size of each local site). This rate is sharper than that of model parameter averaging and its variants, implying the higher tolerance of ReBoot with respect to data splits to maintain the full-sample rate. Our simulation study demonstrates the statistical advantage of ReBoot over competing methods. Finally, we propose FedReBoot, an iterative version of ReBoot, to aggregate convolutional neural networks for image classification. FedReBoot exhibits substantial superiority over Federated Averaging (FedAvg) within early rounds of communication.

Popularity bias is a long-standing challenge in recommender systems. Such a bias exerts detrimental impact on both users and item providers, and many efforts have been dedicated to studying and solving such a bias. However, most existing works situate this problem in a static setting, where the bias is analyzed only for a single round of recommendation with logged data. These works fail to take account of the dynamic nature of real-world recommendation process, leaving several important research questions unanswered: how does the popularity bias evolve in a dynamic scenario? what are the impacts of unique factors in a dynamic recommendation process on the bias? and how to debias in this long-term dynamic process? In this work, we aim to tackle these research gaps. Concretely, we conduct an empirical study by simulation experiments to analyze popularity bias in the dynamic scenario and propose a dynamic debiasing strategy and a novel False Positive Correction method utilizing false positive signals to debias, which show effective performance in extensive experiments., Comment: Accepted at KDD 2022 Workshop on Data Science and Artificial Intelligence for Responsible Recommendations (DS4RRS)

Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant cross-sectional shapes (such as metasurface units). However, when the cross-sectional shape varies even mildly (such as a taper), existing semi-analytical methods suffer from high computational cost. We show that the existing methods can be viewed as a zeroth-order approximation with respect to the structure's cross-sectional variation. We instead derive a high-order perturbative expansion with respect to the cross-sectional variation. Based on this expansion, we propose a new semi-analytical method that is fast to compute even in presence of large cross-sectional shape variation. Furthermore, we design an algorithm that automatically discretizes the structure in a way that achieves a user specified accuracy level while at the same time reducing the computational cost.

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and signal sparsity, we fix the minimum signal magnitude at the information-theoretic optimal rate and investigate the asymptotic selection accuracy of best subset selection (BSS) and marginal screening (MS) procedures. We show that despite the ideal setup, somewhat surprisingly, marginal screening can fail to achieve exact recovery with probability converging to one in the presence of heterogeneous signals, whereas BSS enjoys model consistency whenever the minimum signal strength is above the information-theoretic threshold. To mitigate the computational intractability of BSS, we also propose an efficient two-stage algorithmic framework called ETS (Estimate Then Screen) comprised of an estimation step and gradient coordinate screening step, and under the same scaling assumption on sample size and sparsity, we show that ETS achieves model consistency under the same information-theoretic optimal requirement on the minimum signal strength as BSS. Finally, we present a simulation study comparing ETS with LASSO and marginal screening. The numerical results agree with our asymptotic theory even for realistic values of the sample size, dimension and sparsity., Comment: 46 pages, 3 figures

Fusing regression coefficients into homogenous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called $L_0$-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called grouping sensitivity that underpins the difficulty of recovering the true groups. We show that $L_0$-Fusion achieves grouping consistency under the weakest possible requirement of the grouping sensitivity: if this requirement is violated, then the minimax risk of group misspecification will fail to converge to zero. Moreover, we show that in the high-dimensional regime, one can apply $L_0$-Fusion coupled with a sure screening set of features without any essential loss of statistical efficiency, while reducing the computational cost substantially. On the algorithmic aspect, we provide a MIO formulation for $L_0$-Fusion along with a warm start strategy. Simulation and real data analysis demonstrate that $L_0$-Fusion exhibits superiority over its competitors in terms of grouping accuracy.

Session-based recommender systems aim to improve recommendations in short-term sessions that can be found across many platforms. A critical challenge is to accurately model user intent with only limited evidence in these short sessions. For example, is a flower bouquet being viewed meant as part of a wedding purchase or for home decoration? Such different perspectives greatly impact what should be recommended next. Hence, this paper proposes a novel session-based recommendation system empowered by hypergraph attention networks. Three unique properties of the proposed approach are: (i) it constructs a hypergraph for each session to model the item correlations defined by various contextual windows in the session simultaneously, to uncover item meanings; (ii) it is equipped with hypergraph attention layers to generate item embeddings by flexibly aggregating the contextual information from correlated items in the session; and (iii) it aggregates the dynamic item representations for each session to infer the general purpose and current need, which is decoded to infer the next interesting item in the session. Through experiments on three benchmark datasets, we find the proposed model is effective in generating informative dynamic item embeddings and providing more accurate recommendations compared to the state-of-the-art.

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on the design matrix. Lying at the heart of the proof is a covering number bound for the family of projection operators corresponding to the subspaces spanned by the design. By leveraging this complexity result, we perform a power analysis for a permutation test on the existence of a low-rank signal under the high-dimensional trace regression model. We show that the permutation test based on the rank-constrained least-squares estimator achieves non-trivial power with no assumptions on the minimum (restricted) eigenvalue of the covariance matrix of the design. Finally, we use alternating minimization to approximately solve the rank-constrained least-squares problem to evaluate its empirical in-sample prediction risk and power of the resulting permutation test in our numerical study.

The past decade has witnessed a surge of endeavors in statistical inference for high-dimensional sparse regression, particularly via de-biasing or relaxed orthogonalization. Nevertheless, these techniques typically require a more stringent sparsity condition than needed for estimation consistency, which seriously limits their practical applicability. To alleviate such constraint, we propose to exploit the identifiable features to residualize the design matrix before performing debiasing-based inference over the parameters of interest. This leads to a hybrid orthogonalization (HOT) technique that performs strict orthogonalization against the identifiable features but relaxed orthogonalization against the others. Under an approximately sparse model with a mixture of identifiable and unidentifiable signals, we establish the asymptotic normality of the HOT test statistic while accommodating as many identifiable signals as consistent estimation allows. The efficacy of the proposed test is also demonstrated through simulation and analysis of a stock market dataset.

The learning-to-rank problem aims at ranking items to maximize exposure of those most relevant to a user query. A desirable property of such ranking systems is to guarantee some notion of fairness among specified item groups. While fairness has recently been considered in the context of learning-to-rank systems, current methods cannot provide guarantees on the fairness of the proposed ranking policies. This paper addresses this gap and introduces Smart Predict and Optimize for Fair Ranking (SPOFR), an integrated optimization and learning framework for fairness-constrained learning to rank. The end-to-end SPOFR framework includes a constrained optimization sub-model and produces ranking policies that are guaranteed to satisfy fairness constraints while allowing for fine control of the fairness-utility tradeoff. SPOFR is shown to significantly improve current state-of-the-art fair learning-to-rank systems with respect to established performance metrics., Comment: Under review

Volatility forecasting is crucial to risk management and portfolio construction. One particular challenge of assessing volatility forecasts is how to construct a robust proxy for the unknown true volatility. In this work, we show that the empirical loss comparison between two volatility predictors hinges on the deviation of the volatility proxy from the true volatility. We then establish non-asymptotic deviation bounds for three robust volatility proxies, two of which are based on clipped data, and the third of which is based on exponentially weighted Huber loss minimization. In particular, in order for the Huber approach to adapt to non-stationary financial returns, we propose to solve a tuning-free weighted Huber loss minimization problem to jointly estimate the volatility and the optimal robustification parameter at each time point. We then inflate this robustification parameter and use it to update the volatility proxy to achieve optimal balance between the bias and variance of the global empirical loss. We also extend this Huber method to construct volatility predictors. Finally, we exploit the proposed robust volatility proxy to compare different volatility predictors on the Bitcoin market data. It turns out that when the sample size is limited, applying the robust volatility proxy gives more consistent and stable evaluation of volatility forecasts., Comment: 48 pages

The early solution path, which tracks the first few variables that enter the model of a selection procedure, is of profound importance to scientific discoveries. In practice, it is often statistically hopeless to identify all the important features with no false discovery, let alone the intimidating expense of experiments to test their significance. Such realistic limitation calls for statistical guarantee for the early discoveries of a model selector. In this paper, we focus on the early solution path of best subset selection (BSS), where the sparsity constraint is set to be lower than {the true sparsity}. Under a sparse high-dimensional linear model, we establish the sufficient and (near) necessary condition for BSS to achieve sure early selection, or equivalently, zero false discovery throughout its early path. Essentially, this condition boils down to a lower bound of the minimum projected signal margin that characterizes the gap of the captured signal strength between sure selection models and those with spurious discoveries. Defined through projection operators, this margin is independent of the restricted eigenvalues of the design, suggesting the robustness of BSS against collinearity. Moreover, our model selection guarantee tolerates reasonable optimization error and thus applies to near best subsets. Finally, to overcome the computational hurdle of BSS under high dimension, we propose the "screen then select" (STS) strategy to reduce dimension for BSS. Our numerical experiments show that the resulting early path exhibits much lower false discovery rate (FDR) than LASSO, MCP and SCAD, especially in the presence of highly correlated design. We also investigate the early paths of the iterative hard thresholding algorithms, which are greedy computational surrogates for BSS, and which yield comparable FDR as our STS procedure.