Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector norm, whic…
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48 results for “computational thresholds”
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple non-overlapping) signal submatrix…
Study stability thresholds of big line bundles, proving bounds and generalizing results.
problem Stability thresholds of big line bundles and their asymptotic behavior.
method Explicit bounds on error terms, using quasi-monomial valuations to compute stability thresholds.
result Proves Jin--Rubinstein--Tian's questions affirmatively.
Study on detecting and recovering hidden dense cycles in random graphs.
problem Detecting and recovering hidden dense cycles in random graphs.
method Information-theoretic analysis of thresholds for detection and recovery.
result Characterization of information-theoretic thresholds for detection and recovery.
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created wh…
Noise makes learning linear thresholds hard, but algorithms can still learn near-optimal thresholds.
problem Learning linear thresholds in noisy data.
method Exploiting natural assumptions on data-generating process.
result Efficient learning of near-optimal linear thresholds is still possible with small data even in the presence of noise.
Conservative Likelihood Ratio Estimator for Infrequent Data Slightly above a Frequency Thresholdstat.ML
Proposes a conservative LR estimator for infrequent data near a frequency threshold.
problem Overestimation of likelihood ratios for infrequent data near a frequency threshold.
method Conservative likelihood ratio estimator for frequencies slightly above a threshold.
result Improves prediction accuracy in named entity context prediction.
A new adaptive binarization technique using fuzzy integrals improves image quality.
problem Improving image thresholding quality.
method FLAT (Fuzzy Local Adaptive Thresholding) based on fuzzy integrals.
result The proposed FLAT method produces better image quality than traditional algorithms and neural networks.
We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical thresh…
Finite generation for valuations computing stability thresholds and applications to K-stabilitymath.AG
Proves finitely generated associated graded rings for valuations on log Fano pairs.
problem Stability thresholds of log Fano pairs.
method Proves finite generation of associated graded rings for valuations.
result Log Fano pairs are uniformly K-stable if their stability threshold is less than a certain value.
The article examines different thresholding methods for improving PAM algorithm in cancer classification.
problem High-dimensional classification with too many features selected by PAM.
method Extends PAM with hard and order thresholding methods and a deep search algorithm.
result Improved cancer status prediction accuracy and smaller number of features.
Paper discusses new stochastic algorithms for sparse signal recovery.
problem Sparse signal recovery in medical imaging and remote sensing.
method Proposes and analyzes stochastic natural thresholding algorithms.
result Demonstrates improved performance of StoNT algorithms.
The paper discusses thresholds and bounds for accuracy in binary classification systems.
problem The accuracy of binary classification systems and its dependence on prevalence.
method Analyzing the precision-prevalence curve and negative predictive value-prevalence curve to find thresholds and bounds.
result Thresholds ( and ) bound various accuracy metrics (Fβ, F1, FM, MCC) and the ratio of maximum accuracy to prevalence.
The paper establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
problem Learning Latent Markov Decision Processes (LMDPs) with separated components.
method The paper considers various notions of separation and establishes a nearly-sharp statistical threshold for efficient learning. It also presents a quasi-polynomial algorithm with time complexity scaling in terms of the statistical threshold under a weaker assumption of separability under the optimal policy, and a near-matching time complexity lower bound under the exponential time hypothesis.
result Establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
Target search optimization by threshold resettingcond-mat.stat-mech
Optimizes search times by resetting agents when a threshold is reached.
problem Improving search efficiency in systems with thresholds.
method Develops a framework for correlated stochastic processes with threshold resetting.
result Optimal resetting can prevent larger losses and is applicable to various stochastic systems.
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for sum-of-squares and related to the method of moments. Our focus is on sample complexity bo…
LinearAPT optimizes decision-making under resource constraints for a linear threshold problem.
problem Optimizing sequential decisions with a linear threshold under resource limitations.
method LinearAPT, an adaptive algorithm for fixed-budget TLB problem.
result LinearAPT achieves theoretical upper bounds and robust performance on various datasets.
New findings on community recovery in SBM with many communities.
problem Determining community recovery conditions in SBM with more than sqrt(n) communities.
method Constructing motifs and counting them to prove community recovery above the proposed threshold.
result Proving community recovery above the proposed threshold in SBM with K >= sqrt(n) communities.
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
problem Understanding the statistical-computational gap in binary perceptron models.
method Application of fully lifted random duality theory (fl RDT) to uncover structural changes.
result Numerical estimates of constraint density thresholds align with theoretical predictions.
The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard dictionaries often lead to non-optimal performance when used for computing thresholde…
Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.
problem Detecting and recovering dense cycles in Erdős-Rényi graphs.
method Characterization of computational thresholds for detection and recovery using low-degree polynomial algorithms.
result A gap exists between the detection and recovery thresholds for certain parameter regimes.
Adaptive Threshold Samplingstat.ML
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the sampling probabilities via a collection of thresholds.In general, adaptive samp…
Ridge regression is revisited with debiasing and thresholding, offering advantages over Lasso.
problem High-dimensional data challenges classical ridge regression's sparsity detection and bias issues.
method Debiasing and thresholding ridge regression, introducing a wild bootstrap for confidence regions and hypothesis testing, and a hybrid bootstrap for prediction intervals.
result Debiased and thresholded ridge regression can offer similar performance to thresholded Lasso and may be preferable in some settings.
We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano variety degenerates to a uniquely determined twisted K-polystable Fan…
Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in…
Statistical-computational gap found in aligning multiple Gaussian graphs.
problem Aligning multiple Gaussian graphs with unknown signals.
method Generalized informational threshold and computational barrier analysis.
result Existence of a statistical-computational gap in multiple Gaussian graph alignment.
Azure (the cloud service provided by Microsoft) is composed of physical computing units which are called nodes. These nodes are controlled by a software component called Fabric Controller (FC), which can consider the nodes to be in one of many different states such as Ready, Unhealthy, Booting, etc. Some of these state…
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
Threshold tests have recently been proposed as a useful method for detecting bias in lending, hiring, and policing decisions. For example, in the case of credit extensions, these tests aim to estimate the bar for granting loans to white and minority applicants, with a higher inferred threshold for minorities indicative…
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…
Study uses supercomputers to improve financial predictions.
problem Improving financial predictions through better exploration of data.
method Refactored and ran algorithm on Fugaku supercomputer, exploring more rules.
result Increasing the number of explored rules improves predictive performance.
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
Fault-tolerant neural networks inspired by biological error correction codes.
problem Achieving reliable computation with unreliable neurons.
method Using biological error correction codes from grid cells in the mammalian cortex to develop a fault-tolerant neural network.
result Noisy biological neurons operate below a fault-tolerance threshold, suggesting a mechanism for reliable computation in the brain.
SoftAD improves classification accuracy with less fine-tuning and fewer computational costs.
problem Improving classification accuracy with less fine-tuning and fewer computational costs.
method SoftAD is a softened, pointwise mechanism that downweights borderline points and limits the effects of outliers.
result SoftAD achieves classification accuracy competitive with flooding and SAM, with a smaller loss generalization gap and model norm.
The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study the information-theoretic and computational tradeoffs that arise in combinatori…
A new algorithm improves sample complexity for thresholding in Monte Carlo Tree Search.
problem Determining if the root node value of a tree is at least a given threshold.
method Developed a δ-correct sequential sampling algorithm based on the Track-and-Stop strategy.
result Ratio-based modification of D-Tracking strategy reduces sample complexity and computational cost.
Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completionstat.ML
The sparse inverse covariance estimation problem is commonly solved using an -regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A recent line of results showed--under mild assumptions--that the graphical lasso esti…
Study active learning of PTFs with derivative access.
problem Active learning of polynomial threshold functions (PTFs).
method Algorithm for active learning degree- univariate PTFs with derivative access.
result Computational efficient algorithm for active learning degree- univariate PTFs.
DIET-SNN optimizes SNNs for faster, lower-energy image classification.
problem High inference latency and inefficient input encoding in SNNs.
method End-to-end backpropagation to optimize membrane leak and firing threshold.
result Achieves top-1 accuracy of 69% on ImageNet with 5 timesteps and 12x less compute energy.
A simple thresholding technique improves graph selection in neural connectivity studies.
problem Graphical model selection for functional neural connectivity in the presence of latent variables.
method Apply a hard thresholding operator to graphical Lasso, neighborhood selection, or CLIME estimators.
result Thresholded estimators outperform existing methods in graph selection consistency and empirical results.
The global log canonical threshold (or Tian's alpha-invariant) plays an important role in the geometry of Fano varieties. Tian showed that Fano manifolds with big alpha-invariant can be equipped with a Kahler-Einstein metric. In recent years Donaldson drafted a programme to determine when a smooth Fano variety X admits…
In this work, a heuristic as operational tool to estimate the lactate threshold and to facilitate its integration into the training process of recreational runners is proposed. To do so, we formalize the principles for the lactate threshold estimation from empirical data and an iterative methodology that enables experi…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …
In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…
We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met,…
Monotone neural networks can approximate and interpolate functions efficiently.
problem Understanding the efficiency and expressiveness of monotone neural networks.
method Solving the monotone interpolation problem using depth-4 networks and comparing size bounds with arbitrary networks.
result Monotone neural networks can approximate and interpolate functions efficiently, but may require exponential size in high dimensions.
When to Trust Confidence Thresholding: Calibration Diagnostics for Pseudo-Labelled Regressionstat.ME
The study examines when to trust confidence thresholding in pseudo-labelling regression.
problem Calibrated probabilities from classifiers used for pseudo-labelling need careful handling to avoid bias in downstream regression.
method Developed a diagnostic apparatus to predict and bound the bias induced by confidence thresholding, derived a closed-form expression for the attenuation bias.
result The bias can be predicted from the residual score variance , motivating a structural separation between classifier features and downstream controls.