Title: $\text{G}^2\text{M}$: A Generalized Gaussian Mirror Method to Boost Feature Selection Power
Venue: NeurIPS 2025
Accepted: yes
Keywords: Feature Selection

FDR Control

Hypothesis Testing; Gaussian Mirror; Boosting Power
Abstract: Recent advances in false discovery rate (FDR)-controlled feature selection methods have improved reliability by effectively limiting false positives, making them well-suited for complex applications. A popular FDR-controlled framework called data splitting uses the "mirror statistics" to select features. However, we find that the unit variance assumption on mirror statistics could potentially limit the feature selection power. To address this, we generalize the mirror statistics in the Gaussian mirror framework and introduce a new approach called "generalized Gaussian mirror" ($\text{G}^2\text{M}$), which adaptively learns the variance and forms new test statistics.  We demonstrate both theoretically and empirically that the proposed test statistics achieve higher power than those of Gaussian mirror and data splitting. Comparisons with other FDR-controlled frameworks on synthetic, semi-synthetic, and real datasets highlight the superior performance of the $\text{G}^2\text{M}$ method in achieving higher power while maintaining FDR control. These findings suggest the potential for the $\text{G}^2\text{M}$ method for practical applications in real-world problems. Code is available in https://github.com/skyve2012/G2M.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a generalized gaussian mirror method for feature selection, which addresses the unit variance constraint on the mirror test statistics. Two algorithms are proposed, one for known coefficient scale and the other for unknown. The authors show theoretically that the proposed G2M method is more powerful than existing methods. Extensive numerical validates their theoretical claims and show superiority of the G2M method.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n\n1. The theoretical claims are concise and formulated in an easy-to-follow way.\n2. The authors have conducted extensive and detailed numerical experiments to validate their theoretical claims and the superiority of their proposed G2M.\n\nWeakness:\n\n1. With a rich background of the feature selection problem and extensive existing methods mentioned by the authors, the paper does not formulate or describe any existing method in the main text. For readers who are not familiar with the field, it could be quite difficult to follow and even more difficult to figure out the contribution made by the authors.\n2. In comparison, the details for simulation settings and implementation take too much space. I believe it is the main reason for weakness 1 since the page limit is 9. I strongly recommend the authors to delay unnecessay details of the experiments to the appendix and save more space for the introduction part.\n\nQUESTIONS:\n1. Since the authors assume a linear model between X and Y, is G2M valid for general regression models? Or is it possible to extend G2M to general models?\n2. The coefficients $\\beta^+$ and $\\beta^-$ are used without clear definitions. I have noticed a rough definition in the appendix but they are frequently used in the methodology part. It would be better to move their definitions to the main text before their usage.\n3. Although the method is based on existing works that ensure FDR control, it would be better to explicitly formulate this property in a short theorem. It might be a straightforward result or even only a proposition, but showing this issue is worthy since there are also many intuitive methods for feature selection which has no error rate control guarantee.\n\n\nI will be willing to raise my score if the paper is reformulated appropriately.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the problem of variable selection under false discovery rate (FDR) control for linear regression models. The authors propose a generalized Gaussian mirror ($\\text{G}^2$M) test statistics to study the feature selection problem. They established rigorous theoretical guarantees for the $\\text{G}^2$M statistics, including the entry-wise UMP properties and the advantage over existing statistics. Algorithms are proposed to handle both the case where one has access to true nonnull $\\beta_j$'s and the estimation in practice. Substantial empirical simulations are then conducted based on the estimation algorithm, which shows the advantages of the $\\text{G}^2$M statistics in terms of testing power and FDR control.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n\n1.  The paper provided a good motivation for why one might care to consider using the $\\text{G}^2$M statistics for the variable selection problem under false discovery rate (FDR) control. \n \n2. The theoretical foundation is strong, with clear lemmas and theorems providing a closed-form $\\text{G}^2$M statistics that is UMP and is more powerful over existing statistics including the Gaussian mirror and the data-splitting test statistics.\n  \n3. The methodology provides greater empirical power than multiple benchmarking methods in both the synthetic and the semi-synthetic simulation settings.\n\n\n\n\n\nWeaknesses: \n\n1. The paper does not discuss whether the proposed $\\text{G}^2$M test statistics have an intuitive interpretation, which may be of interest in the case of real-world data.\n \n2. There is still some ambiguity concerning the difference between $\\text{G}^2$M and $\\text{G}^2\\text{M}\\dagger$. Given that the highest statistical power is predominantly achieved using $\\text{G}^2\\text{M}\\dagger$ instead of $\\text{G}^2$M, further justification is required to substantiate the selection of the $\\tau_q$ in Eq.3 (assuming it is the equation between line 215 and 216) as the optimal threshold.\n \n3. It would be desirable to have at least one more real case study in section 3.3 as the current example does not sufficiently illustrate the comparative advantages of the proposed method over existing approaches.\n\nQUESTIONS:\n1.  In section 3.1, the selection of $\\rho=\\{0.6,0.7\\}$ needs some further justification.\n  \n2. The simulation using the Copula model on page 6 needs additional clarification, given that the reader may not possess prior knowledge of this methodology.\n\nTypos: \n\n1. Page 7, line 214: Eq. (3) cannot be found in the main file (assuming it is the equation between line 215 and 216). \n2. Page 9, line 323: 'An possible' should be 'A possible'\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the task of generating realistic and diverse human motions from natural language descriptions, with a focus on improving generalization across different datasets and motion styles. The authors propose a novel method called MotionAuto, a diffusion-based model that separates the motion generation process into two stages:\n\n1. Text-to-Motion Representation (T2MRep) Generation: Given a text input, the model generates a latent motion representation using a transformer-based architecture with diffusion sampling. This stage learns a distribution over possible motion intents, grounded in the textual description.\n\n2. Motion Decoding: The generated T2MRep is then passed to a motion decoder that reconstructs a full motion sequence using a generalizable motion prior.\n\nA key contribution of the paper is the Generalizable Motion Prior (GMP)—a modular and transferable motion representation trained to model the manifold of realistic human motions independent of specific text annotations or datasets. By disentangling motion prior learning from language grounding, GMP enables zero-shot and few-shot transfer to new datasets and tasks.\n\nThe model is evaluated across multiple datasets (HumanML3D, KIT-ML, and BABEL) and shows superior performance in both standard and cross-dataset generalization settings, with improved diversity, realism, and text-motion alignment compared to strong baselines. Qualitative examples and ablations further support the effectiveness of the modular design and latent representation.\n\nSTRENGTHS AND WEAKNESSES:\n-Strengths\n\n--Quality\n\nSound technical approach: The proposed two-stage architecture, combining text-guided latent representation generation and motion decoding via a generalizable prior, is methodologically well-motivated and executed.\n\nStrong empirical performance: The model shows consistent improvements across standard and cross-dataset evaluations (HumanML3D, KIT-ML, BABEL). Metrics indicate better realism, diversity, and text-motion alignment.\n\nComprehensive evaluation: The authors provide detailed ablation studies and visualizations to justify the design choices. Both quantitative and qualitative results support the claims.\n\n--Clarity\n\nClear presentation: The paper is well-written and logically structured. Figures and diagrams (especially the model overview on page 3) effectively illustrate the pipeline and components.\n\nDefined terminology: Concepts such as T2MRep and GMP are clearly introduced and consistently used.\n\n--Significance\n\nAddresses a key limitation: The work tackles generalization in text-to-motion models—a major hurdle in practical deployment and cross-domain usage.\n\nPractical utility: By decoupling motion learning from text supervision, the proposed framework lowers the annotation burden and increases reusability of pretrained components.\n\n--Originality\n\nNovel modular design: The introduction of GMP as a reusable, disentangled motion prior is a creative and impactful contribution.\n\nDiffusion in latent space: Applying diffusion to a motion-specific latent space (rather than directly to poses or joint angles) adds a fresh perspective on modeling uncertainty in motion generation.\n\n-Weaknesses\n\n--Quality\n\nLimited analysis of failure cases: While success is well-demonstrated, the paper would benefit from a deeper exploration of when or why the model fails (e.g., unusual text prompts or out-of-distribution motion types).\n\nFew details on computational cost: The runtime or training/inference efficiency is not thoroughly reported or compared to baselines, which may matter for real-world adoption.\n\n--Clarity\n\nLatent space interpretability: The nature and structure of the T2MRep and GMP representations could be more explicitly explained or visualized. What semantics, if any, do these latent variables capture?\n\n--Significance\n\nLimited modality diversity: All experiments are in the domain of skeleton-based 3D human motion. It remains unclear how well the approach generalizes to other data modalities (e.g., 2D video motion, gestures, or robotic trajectories).\n\n--Originality\n\nBuilding on recent trends: While the combination is novel, many components—diffusion models, latent space modeling, and modular priors—build upon recent work in motion synthesis and text-to-motion generation. The originality lies in the effective integration and the use of GMP, rather than in new fundamental techniques.\n\nQUESTIONS:\n1. What is the structure and semantics of the T2MRep latent space?\n\nQuestion: Can the authors clarify what kind of information the Text-to-Motion Representation (T2MRep) encodes? Visualizations (e.g., t-SNE or PCA plots) or clustering analyses could help reveal whether semantically similar motions occupy nearby regions in this space. A better understanding of T2MRep's structure would support its interpretability and clarify why diffusion in this space works well.\n\n2. How transferable is the Generalizable Motion Prior (GMP) across domains or tasks?\n\nQuestion: Beyond cross-dataset generalization, have the authors tested GMP in new tasks (e.g., action classification or robotic control) or motion styles (e.g., stylized, multi-agent)? Even preliminary results or discussion about potential use cases would strengthen the claim of “generalizability.” Demonstrating use of GMP outside the training regime would increase confidence in its utility and modularity.\n\n3. What are the failure modes of the proposed system?\n\nQuestion: In what scenarios does MotionAuto fail to generate meaningful or aligned motions (e.g., under ambiguous, long, or compound text prompts)? Including a qualitative analysis or examples of such failures can help guide future improvements and clarify the method’s limits. If failure cases are rare or easily explained, this would reinforce the system's robustness.\n\n4. How does the method perform under low-resource settings?\n\nQuestion: Have the authors measured how MotionAuto performs when fine-tuned or trained on smaller datasets, especially when GMP is reused? A few-shot or low-data experiment would be helpful to demonstrate whether GMP meaningfully reduces the data burden. Positive results here would further validate one of the paper's key motivations: generalization with limited supervision.\n\n5. What is the computational efficiency compared to baselines?\n\nQuestion: What are the training and inference time comparisons between MotionAuto and other leading methods like MDM or MotionDiffuse? Including runtime or memory usage benchmarks (even briefly in the appendix) would give a more complete picture of the model’s practicality. If the proposed method is competitive in terms of resources, it would increase its appeal for broader deployment.\n\nLIMITATIONS:\nWhile the technical contributions are well-developed, the paper does not sufficiently address potential limitations or negative societal impacts of text-to-motion generation. Here are some suggestions for improvement:\n\n- Ethical Concerns: Consider discussing risks such as misuse in surveillance, deepfake-style animations, or biased motion generation (e.g., due to dataset imbalances).\n\n- Representation Bias: Acknowledge if datasets like HumanML3D or KIT-ML might overrepresent specific motion types, body types, or cultures, which could affect generalizability and fairness.\n\n- Physical Safety: For applications in robotics or avatar control, incorrect motion generation could cause physical harm or user confusion. This should be mentioned as a risk.\n\n- Failure Mode Transparency: Limitations in generating rare, multi-agent, or highly dynamic motion types are not explicitly addressed and would be important for understanding the boundaries of the method’s reliability.\n\nIncluding even a brief discussion in the main paper or appendix would enhance transparency and responsibility.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-04"}

comments: SUMMARY:
The paper identifies the limitation of existing mirror statistics and presents a Generalized Gaussian Mirror method to enhance feature selection. The method is compared with multiple FDR related methods across different datasets (synthetic and real world), which shows efficacy in controlling FDR while achieving high power.

STRENGTHS AND WEAKNESSES:
Strengths:   
+ The related work covered sufficient works with proper discussion linking all related works, and motivating the proposed method.
+ Method is evaluated on multiple datasets, both synthetic and real world data, and compared with state-of-the-art methods. 
+ Problem is well motivated with clear background and rationale. 
+ The paper includes detailed proofs for each part of the method.

Weaknesses:   
- The paper address the limitation of existing mirror statistics, novelty is not that significant. 
- The experiment part can be enhanced with some significance test on the result comparing with other methods. 
- It's good that the paper points out the limitation of assuming normal distribution on the fitting coefficients, however, the limitation is still there. It would be good to discuss more on how this normal distribution can be lifted/resolved.

QUESTIONS:
1.It would be good to add rationale on why k-means is selected in estimation algorithm. 

2.The paper references paper 'Shen et al [32]' quite a lot, regarding problem set up, method, experiment setting, and result discussion. It would be good to add more discussion and clarifications on what's the novelty/originality of this paper compared with existing 'Shen et al [32]'

3.some discussion on the method complexity would be good and on how it compares with other methods in terms of computational complexity.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-31