Rank minimization has attracted a lot of attention due to its robustness in data recovery. To overcome the computational difficulty, rank is often replaced with nuclear norm. For several rank minimization problems, such a replacement has been theoretically proven to be valid, i.e., the solution to nuclear norm minimiza…
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48 results for “ranking validity”
Proposes a method for explaining ranking decisions in learning systems.
problem Limited work on interpreting ranking decisions from learning systems.
method Model agnostic local explanation method using optimization to maximize validity.
result Approach outperforms other methods in validity across different LTR models.
Replicated and validated Rank-N-Contrast for robust regression.
problem Deep regression models struggle with continuous sample orders.
method Contrastive learning of continuous representations by ranking samples.
result Improved performance and robustness of RNC framework.
Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compressionstat.ML
Optimizes tensor rank selection for neural network compression.
problem Finding optimal tensor rank for regression models.
method Analyzes population expressions for training-testing discrepancy under Gaussian design.
result Optimal rank minimizes prediction error and aligns with cross-validation.
Paper proposes HCDC to improve hyperparameter search efficiency.
problem Poor generalizability of dataset condensation across different hyperparameters.
method HCDC algorithm that matches hyperparameter gradients for synthetic validation dataset.
result HCDC effectively maintains validation-performance rankings of models.
The paper validates a method for recovering over-parameterized matrices and images from noisy measurements.
problem Recovering a low-rank matrix from noisy measurements when the rank is unknown.
method Using gradient descent with small random initialization on a nonconvex objective function built from a rank-overspecified factored representation of the matrix variable.
result Gradient descent iterations converge to the ground-truth matrix under certain conditions and can be stopped efficiently to detect a nearly optimal estimator.
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing …
Learning the true ordering between objects by aggregating a set of expert opinion rank order lists is an important and ubiquitous problem in many applications ranging from social choice theory to natural language processing and search aggregation. We study the problem of unsupervised rank aggregation where no ground tr…
New ACV method speeds up CV in high dimensions with approximate low-rank data.
problem Accurate model assessment in high-dimensional, large data settings with expensive algorithms.
method Developed a new ACV algorithm that uses low-rank approximations of the Hessian matrix.
result The new method is fast and accurate in the presence of approximate low-rank data.
Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisonsstat.ME
Low-rank framework for task-specific LLM ranking from sparse comparisons.
problem Challenges in reliable task-specific ranking of LLMs under sparse, imbalanced comparisons.
method Low-rank modeling of task-by-model ability matrix, max-norm accurate estimator, task-wise top-K recovery guarantees, uncertainty quantification framework.
result Improves sample efficiency and produces tighter, better-calibrated ranking certificates.
Develops efficient method for updating models with small data changes.
problem Efficiently updating models when data changes (e.g., adding/removing instances/features).
method Generalized Low-Rank Update (GLRU) for non-linear estimators.
result Provides updated solutions with computational complexity proportional to dataset changes.
This paper presents a Bayesian method for estimating the rank of a low-rank tensor model of joint PMF.
problem Estimating the rank of a low-rank tensor model of joint PMF from observed data.
method Bayesian framework for estimating low-rank components and rank simultaneously, using variational inference.
result Automatic rank detection and improved estimation accuracy compared to cross-validation methods.
This work establishes always-valid risk bounds for online matrix completion.
problem Challenges in establishing always-valid concentration inequalities for online matrix completion.
method Combines non-asymptotic martingale concentration and regularized low-rank matrix regression.
result Establishes always-valid risk bound process for online matrix completion.
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature …
Tournament Leave-pair-out Cross-validation for Receiver Operating Characteristic (ROC) Analysisstat.ML
Receiver operating characteristic (ROC) analysis is widely used for evaluating diagnostic systems. Recent studies have shown that estimating an area under ROC curve (AUC) with standard cross-validation methods suffers from a large bias. The leave-pair-out (LPO) cross-validation has been shown to correct this bias. Howe…
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
IRMAE learns compact latent spaces by minimizing rank.
problem Learning compact latent representations in autoencoders.
method Implicitly minimizes the rank of the covariance matrix through gradient descent in multi-layer linear networks.
result Demonstrates validity on image generation and representation learning tasks.
The paper reviews exchangeability and its implications for conformal prediction and rank tests.
problem Ensuring distribution-free predictive inference in machine learning and statistics.
method Explains exchangeability and its role in conformal prediction and rank tests.
result Discovers similarities between conformal prediction and rank tests based on exchangeability.
Hierarchical framework for model evaluation on leaderboards
problem Uncertainty and variability in model performance across tasks
method Hierarchical framework with task-level and leaderboard-level rank prediction intervals
result Statistically valid and informative model rank intervals
New ranking algorithms improve online content delivery by learning from click data.
problem Bias in ranking systems due to production system biases.
method Proposed novel extensions of LinUCB and Linear Thompson Sampling algorithms to handle position-based click model.
result Validated the proposed algorithms through offline and online experiments.
This is the appendix of the paper [T. Arias-Marco, Constant Jacobi osculating rank of , Arch. Math. (Brno) 45 (2009), 241--254] where we obtain an interesting relation between the covariant derivatives of the Jacobi operator valid for all geodesic on the flag manifold $M^6=U(3)/(U(1…
New gossip algorithms improve robustness of rank-based statistics in decentralized systems.
problem Ensuring robustness in decentralized AI and edge intelligence systems, especially in the presence of corrupted or adversarial data.
method Developed asynchronous gossip algorithms for computing rank-based statistics.
result First convergence rate bound for asynchronous gossip-based rank estimation.
New insights into attention mechanisms reveal dramatic trade-offs between rank and heads.
problem Dramatic trade-offs between rank and number of heads in attention mechanisms.
method Presented a simple target function and proved theoretical limits.
result Full-rank attention is necessary for long contexts, while low-rank is sufficient for short ones.
A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper. The special structure of low rank kernels with a controlled model size brings sparsity as well as computational efficiency to the proposed model. Meanwhile, a two-step optimization al…
In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy near-optimal error bounds under assumptions on the rank, coherence, and spikiness of B…
Counterfactual Cross-Validation: Stable Model Selection Procedure for Causal Inference Modelsstat.ML
We study the model selection problem in conditional average treatment effect (CATE) prediction. Unlike previous works on this topic, we focus on preserving the rank order of the performance of candidate CATE predictors to enable accurate and stable model selection. To this end, we analyze the model performance ranking …
LEARNER improves low-rank matrix estimation using source population data.
problem Improving low-rank matrix estimation in target populations with diverse data sources.
method LEARNER uses similarity in latent spaces between source and target populations to enhance estimation.
result LEARNER often outperforms benchmark methods, especially with higher signal-to-noise ratios in the source population.
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
The paper addresses privacy in rank aggregation using randomized responses.
problem Preserving privacy while aggregating pairwise rankings.
method Adaptive debiasing method for randomized response rankings.
result Established minimax rates for estimation errors and optimal privacy guarantees.
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
problem Determining the latent dimensions (ranks) in tensor factorization models.
method Prior predictive moment matching to transform moment matching conditions into a log-linear system of equations.
result Identifies which tensor models have identifiable ranks and derives rank estimators.
Paper discusses extending Gini score for tied rankings and case weights.
problem Extending Gini score for tied rankings and case weights.
method Discuss and adapt Gini score for ties and case weights.
result Gini score can be used for tied rankings and case weights.
GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.
problem Efficient fine-tuning of large language models with limited computational resources.
method GeLoRA computes intrinsic dimensionality to adaptively select LoRA ranks, balancing expressivity and efficiency.
result GeLoRA consistently outperforms recent baselines within the same parameter budget on multiple tasks.
There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby alleviating the overfitting and curse of dimensionality problems in the conventio…
The paper optimizes A/B tests by balancing lift and cost in large-scale settings.
problem Balancing lift and cost in A/B tests for large-scale experimentation.
method Empirical Bayes approach using a greedy knapsack algorithm to rank experiments based on lift-to-cost ratio, incorporating local false discovery rate (lfdr).
result The proposed method maximizes expected profit while controlling false discovery rate, demonstrating superior performance in large-scale settings.
Two-stage risk control for ranked retrieval systems.
problem Assessing prediction uncertainty and risk control in sequential machine learning systems.
method Developed two-stage risk control methods based on LTT and CRC frameworks, leveraging sequential nature of retrieval and ranking phases.
result The proposed methods provide theoretical guarantees and reduce computational burden compared to prior work.
Improves CRRR for better mobility analysis with DCTM.
problem Unclear interpretation of RRRX parameters.
method Uses DCTM for conditional ranks, cross-fitting, and asymptotic theory.
result Clearer interpretation and improved accuracy in mobility analysis.
Validity of Feature Importance in Low-Performing Machine Learning for Tabular Biomedical Datastat.ML
This paper shows feature importance remains valid even in low-performing models.
problem Feature importance validity in low-performing machine learning models for biomedical data.
method Experiments with synthetic and real biomedical datasets to compare feature rank stability under different data reductions.
result Feature importance can be maintained even at low performance levels if data size is adequate.
The study proves a conjecture about arborescent links with many twigs.
problem Proving the meridional rank conjecture for arborescent links.
method Using an upper bound on the bridge number in terms of the maximal number of link components of the underlying tree.
result Proves the meridional rank conjecture for arborescent links with specific properties.
Paper proposes a cost-sensitive conformal training method with provably controllable learning bounds.
problem Uncertainty quantification and learning bounds in conformal prediction.
method Cost-sensitive conformal training algorithm that minimizes the expected size of prediction sets using rank weighting.
result Theoretical analysis shows tightness between weighted objective and expected size of conformal prediction sets.
Proposes a low-rank PGD attack for more efficient adversarial training.
problem Efficiency and effectiveness of adversarial training methods.
method Variation of PGD to compute low-rank perturbations.
result Low-rank PGD attacks are more efficient and comparable to traditional attacks.
Develops a support-aware framework for reserve-policy selection in advertising markets.
problem Log-based reserve-price evaluation risks weak support and subgroup harm.
method Support-aware offline decision framework converting logged evidence into certified policies.
result Preserves the best gate-passing policy while eliminating only policies with certified regret.
Paper improves MVSC using tensor low-rank modeling.
problem Improving multi-view spectral clustering.
method Structured tensor low-rank norm for MVSC optimization.
result Proposed method outperforms state-of-the-art methods.
Rank-statistic method approximates -divergences without density-ratio estimation.
problem Approximating -divergences without explicit density-ratio estimation.
method Mapping distribution rank histograms to discrete -divergence and averaging over random projections.
result The rank-statistic estimator is a lower bound of the true -divergence and converges under mild conditions.
Low-rank structure emerges in neural networks during learning.
problem Understanding the evolution of synaptic connectivity over learning.
method Investigated the rank of 3-tensor formed by weight matrices throughout learning.
result Inferred weights are low-tensor-rank and evolve in a fixed low-dimensional subspace.
Method quantifies uncertainty in full ranking with new CP approach.
problem Uncertainty quantification in full ranking with unknown ground truth.
method Transductive Conformal Prediction (CP) method to construct distribution-free bounds.
result Valid prediction sets and false coverage proportion control for full ranking.
New framework assesses LLMs' expertise using nonparametric ranking and confidence diagrams.
problem Evaluating and ranking large language models (LLMs) for alignment and performance.
method Nonparametric contextual ranking, confidence diagram, Gaussian multiplier bootstrap.
result Validated confidence diagram for assessing LLMs' domain-specific expertise.
New method for initializing low-rank neural networks improves performance.
problem Training low-rank neural networks efficiently and accurately.
method Inspired by function approximation, proposes a novel low-rank initialization framework.
result Demonstrates significant gap between spectral and low-rank initialization approaches.