New MCMC algorithm reduces subset selection passes to 2 for optimal k k k -dimensional subspace approximation.
problem Subset selection for k k k -dimensional subspace approximation with ε ε ε -approximation. method MCMC sampling algorithm reducing passes to 2 for p = 2 p=2 p = 2 case, poly(k/ε) size subset. result Subset selection of nearly optimal size in 2 passes, ( 1 + ε ) (1+ε) ( 1 + ε ) approximation. Extends topological theorems to new mapping families.
problem Limitations of existing topological theorems.
method Replaces large subset requirements with smaller subset requirements.
result Extends theorems to m-sphere to n-space mappings with m<n.
Improves performance in various machine learning tasks by reparameterizing subset sampling.
problem Stochastic optimization involving subset sampling is not reparameterizable.
method Continuous relaxation of subset sampling to provide reparameterization gradients.
result Improves performance in instance-wise feature selection, deep stochastic k-nearest neighbors, and parametric t-SNE.
One-pass algorithm finds small subset for ℓ p \ell_p ℓ p subspace approximation with additive error.
problem Finding a small subset of data points for ℓ p \ell_p ℓ p subspace approximation. method One-pass subset selection with additive approximation guarantee for p ∈ [ 1 , ∞ ) p \in [1, \infty) p ∈ [ 1 , ∞ ) . result First one-pass algorithm with additive error for ℓ p \ell_p ℓ p subspace approximation. Subset selection improves weak supervision performance.
problem Optimizing the use of weakly-labeled data.
method Combining pretrained data representations with the cut statistic for subset selection.
result Subset selection improves weak supervision performance by up to 19%.
This paper reduces graph-Laplacian dimensionality for spectral clustering of subsets.
problem High computational cost of graph-Laplacian spectral embedding for large data sets.
method Develops two algorithms for low-dimensional graph-Laplacian representation of target subsets.
result Ensures consistency of target subset clustering with full data set spectral clustering.
Simplified DGPs training by fixing inducing inputs to subset of data.
problem Challenging training of deep Gaussian processes.
method Fixed subset of data for inducing inputs, variational sampling.
result Significant reduction in trainable parameters and computation cost without performance degradation.
Paper tackles fair low-rank approximation and column subset selection.
problem Minimize loss over sub-populations in machine learning.
method Developed algorithms for fair low-rank approximation and fair column subset selection.
result Achieved polynomial time algorithms for fair low-rank approximation.
Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The ℓ 0 \ell_0 ℓ 0 penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of all models. A recent area of considerable interest is to develop efficient algor…
Identifies minimal training subset to flip a prediction.
problem Flipping predictions in machine learning models.
method Extended influence function for relabeling minimal subset.
result Relabeling fewer than 2% of training points can flip a prediction.
Proposes a quantum-inspired algorithm for selecting representative data subsets.
problem Selecting the most representative subset of data from a larger dataset.
method Uses a Quadratic Unconstrained Binary Optimization (QUBO) problem approach.
result Demonstrates the effectiveness of the selector algorithm in finance applications.
Study efficient algorithms for identifying minimum interventional sets to learn causal relationships.
problem Identify the smallest set of interventions to learn causal relationships between a subset of edges.
method Develop algorithms for subset verification and search problems under assumptions of faithfulness, causal sufficiency, and ideal interventions.
result For subset verification, an efficient algorithm is provided to compute a minimum sized interventional set.
Apricot selects subsets from large data sets efficiently using submodular optimization.
problem Efficiently selecting representative subsets from large data sets.
method Submodular optimization with efficient greedy algorithm.
result Strong theoretical guarantees on the quality of selected subsets.
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…
Paper proposes a method to identify negative transfers in multitask learning using surrogate models.
problem Identifying subsets of source tasks that improve target task performance in multitask learning.
method Surrogate modeling to precompute multitask learning performances and approximate them with a linear regression model.
result The approach predicts negative transfers from multiple source tasks to target tasks more accurately than existing methods.
We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N\subset M, the quotient M'=N/A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N\subset M are satisfied for a …
We prove the following Theorem: Let X be a nonempty compact metrizable space, let l 1 ≤ l 2 ≤ . . . l_1 \leq l_2 \leq... l 1 ≤ l 2 ≤ ... be a sequence of natural numbers, and let X 1 ⊂ X 2 ⊂ . . . X_1 \subset X_2 \subset... X 1 ⊂ X 2 ⊂ ... be a sequence of nonempty closed subspaces of X such that for each k in N, d i m Z / p X k ≤ l k < ∞ dim_{Z/p} X_k \leq l_k < \infty d i m Z / p X k ≤ l k < ∞ . Then there exists a compact metriz…
The paper explores how close two Lipschitz functions can be without their difference exceeding a certain bound.
problem Understanding the closeness of two Lipschitz functions and their difference.
method Investigates the relationship between two Lip ( γ ) (\gamma) ( γ ) functions being close throughout a subset of their domain and the bound on the difference's Lipschitz norm. result The Lipschitz norm of the difference between two functions is bounded by a small value when the distance to a subset is small.
Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which subsets of data are processed independently, with very little communication. First, w…
Proposes faster neural network learning by using subsets of training data.
problem Manual design and validation of network topologies is time-consuming.
method Exploits subsets of training data at each incremental training step and performs online hyperparameter selection.
result Significantly reduces overall training time while maintaining performance.
Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another challenge one may encounter is the presence of outliers and contaminations that da…
Improved space management in iterative clustering reduces subset growth without sacrificing performance.
problem Iterative re-clustering of speech segments can lead to unchecked subset growth, compromising performance.
method Integration of a space management strategy into the iterative process of hierarchical clustering.
result No loss in performance in terms of F-measure while guaranteeing space complexity.
DART optimizes subset selection in non-linear bandit problems.
problem Optimizing subset selection in non-linear bandit problems with correlated rewards.
method DART algorithm for combinatorial bandits without individual arm feedback or linearity assumption.
result DART achieves a regret bound of i l d e O ( K K N T ) ilde{\mathcal{O}}(K\sqrt{KNT}) i l d e O ( K K N T ) . ModHiFi identifies critical components for model modification without gradients or loss function.
problem Modifying open weight models without access to training data or loss function.
method Theoretical analysis of Lipschitz-continuous networks, Subset Fidelity metric, and ModHiFi algorithm.
result ModHiFi-P and ModHiFi-U achieve significant performance improvements in model pruning and unlearning.
Paper improves DP-ERM for binary linear classification with large-margin subsets.
problem Differentially private binary linear classification with large-margin subsets.
method Efficient ( ε , δ ) (\varepsilon,δ) ( ε , δ ) -DP algorithm with empirical zero-one risk bound. result Improved empirical zero-one risk bound for binary linear classification.
We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.
problem Optimal low-rank approximation of matrices with ℓ 1 \ell_1 ℓ 1 norm constraints. method Polynomial time column subset selection-based algorithm achieving i l d e O ( k 1 / 2 ) ilde{O}(k^{1/2}) i l d e O ( k 1/2 ) -approximation. result Improved approximation guarantees for ℓ 1 \ell_1 ℓ 1 low-rank approximation. A new algorithm identifies outliers in Gaussian clustering models.
problem Handling outliers in Gaussian model-based clustering.
method OCLUST algorithm removes least plausible points based on subset log-likelihoods until they adhere to a reference distribution.
result OCLUST inherently estimates the number of outliers.
DPPNets approximate DPP sampling with deep learning for efficient subset selection.
problem Efficiently sampling from Determinantal Point Processes (DPPs) with high diversity and quality.
method Developed DPPNets using transformer networks with an inhibitive attention mechanism.
result Samples from DPPNets receive high likelihood under the more expensive DPP alternative, demonstrating efficiency.
We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities t…
Selective removal of data subsets can efficiently unlearn unwanted distributions.
problem Efficiently removing unwanted data subsets without losing important information.
method Formalized as distributional unlearning, using Kullback-Leibler divergence constraints to select a small subset of data.
result Proposed method achieves corresponding log-loss bounds and is quadratically more sample-efficient than random removal.
Differentiable Greedy Networks improve sentence selection for claim verification.
problem Optimal selection of sentences for claim verification in FEVER task.
method Proposes a trainable subset selection algorithm based on submodular optimization and unfolds a greedy algorithm into a computational graph.
result Differentiable Greedy Network (DGN) outperforms other methods in precision and recall.
Estimates reliability of nuclear fuel using advanced modeling techniques.
problem Determining the reliability of TRISO-coated particle fuel, which has small failure probabilities and expensive computational models.
method Coupled active learning, multifidelity modeling, and subset simulation.
result Multifidelity modeling strategies consistently reduce the number of high-fidelity model calls.
Optimizes MCMC output compression by selecting a subset of states.
problem Improving the efficiency of MCMC output compression.
method Greedy minimization of kernel Stein discrepancy for selecting a subset of states.
result The method provides an optimal subset of states for empirical approximation.
A method for finding most influential sets reduces a complex problem to a sequence of simpler top- k k k problems.
problem Identifying most influential subsets in complex models.
method Reduces the problem to a sequence of top- k k k problems using Dinkelbach's method. result The method returns a globally optimal set for the univariate ratio objective, including partial linear models.
Stochastic variational inference (SVI), the state-of-the-art algorithm for scaling variational inference to large-datasets, is inherently serial. Moreover, it requires the parameters to fit in the memory of a single processor; this is problematic when the number of parameters is in billions. In this paper, we propose e…
New method finds open subsets with trivial holonomy for certain geometries.
problem Finding open subsets with trivial holonomy for Cartan geometries.
method Analyzing the behavior of isotropies in model geometries to generalize properties of isolated higher-order fixed points.
result Existence of open subsets with trivial holonomy for Cartan geometries with certain isotropies.
New algorithms select and rank features from MTS without feature extraction.
problem Feature extraction step for MTS classification.
method Directly computes similarity between time series and assesses cluster structure matching labels.
result Techniques match labels well without feature extraction.
New algorithm explores optimally using same primitives as Thompson Sampling.
problem Optimal exploration of unknown parameter vectors with noisy measurements.
method Algorithm leveraging sampling and argmax oracles.
result Achieves exponential convergence rate, optimal among all allocations.
New algorithm scales NDPP learning and inference to large item collections.
problem Memory and runtime limitations in existing NDPP learning and inference algorithms.
method Introduced a new NDPP kernel decomposition for learning and a linear-complexity MAP inference algorithm.
result Our algorithms scale linearly in M M M , matching prior work's predictive performance. Federated learning method selects relevant data to improve model accuracy.
problem Noisy and irrelevant data negatively impacts model training in federated learning.
method Use a benchmark model to evaluate and select relevant data subsets from each client.
result Up to 25% improvement in model accuracy compared to training with all data.
Efficiently removes specific data subsets without retraining for GDPR compliance.
problem Efficiently removing specific data subsets to comply with GDPR regulations.
method Statistical framework for machine unlearning with minimax optimality for squared loss.
result Developed Unlearning Least Squares (ULS) achieving minimax optimality for estimating model parameters.
Paper tackles adaptive sampling for identifying largest gaps between distributions.
problem Adaptive sampling from K distributions to identify the largest gap between any two adjacent means.
method Proposes elimination and UCB-style algorithms, showing minimax optimality.
result UCB-style algorithms require 6-8x fewer samples than non-adaptive sampling.
Ensemble methods have been shown to be an effective tool for solving multi-label classification tasks. In the RAndom k-labELsets (RAKEL) algorithm, each member of the ensemble is associated with a small randomly-selected subset of k labels. Then, a single label classifier is trained according to each combination of ele…
Efficiently clusters large datasets with a subset of landmarks.
problem High computational complexity in subspace clustering for large-scale datasets.
method Selects a subset of landmarks to reduce the clustering problem to linear time.
result Subspace clustering method runs in linear time with respect to the size of the original data.
We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. The spectral algorithm consists of multiple algorithmic steps, named as "{edges}", to which noise cou…
Paper introduces template functions for featurizing persistence diagrams.
problem Featurizing persistence diagrams for machine learning.
method Characterizes compactness, constructs dense subsets of continuous functions.
result Template functions enable supervised learning with persistence diagrams.
Bayesian coresets improved with random sampling and quasi-Newton optimization.
problem Efficiently approximate Bayesian posterior distributions for computationally expensive inference.
method Randomly select a subset of data points, then optimize weights using quasi-Newton method.
result First algorithm with high-probability KL divergence bound on coreset quality.
For proper subsets U of {1,2,...,31} we define and construct U-regular isotopy invariants of the Carter-Rieger-Saito movies (representing knotted surfaces) and use these to show that there are ambient isotopic knotted surfaces represented by movies M1 and M2 for which movie-moves of type 31 are required to get from M1 …