Adaptive algorithm for outlier detection by balancing arm exploration and threshold estimation.
problem Identifying outliers in a set of rewards where the threshold is a function of all rewards.
method Adaptively updated confidence interval for the threshold based on previous rounds' estimates, balancing exploration of individual arms and the outlier threshold.
result Efficient algorithm with reduced sample complexity for outlier detection.
We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an application, we show that they have a Kaehler-Einstein metric if they are general.
We analyze double descent in finite-width neural networks using influence functions.
problem Understanding double descent in finite-width neural networks.
method Using influence functions to derive population loss bounds and investigate loss function effects.
result Derived bounds exhibit double descent behavior at the interpolation threshold.
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type.
This letter improves sparse signal detection from one bit compressed sensing measurements.
problem Sparse signal detection from one bit compressed sensing measurements.
method Extended GLRT detector with optimal quantizer design and a double-detector scheme.
result The double-detector scheme outperforms existing methods in detection performance.
Deep networks generalize well even when they fit training data perfectly, thanks to overparametrization.
problem Understanding generalization in overparametrized deep networks.
method Random features regression, asymptotic analysis, ensemble averaging.
result Bias remains constant beyond the interpolation threshold, while variance components decay with overparametrization.
The paper analyzes the generalization error of random features regression, revealing a double descent curve.
problem Analyzing the generalization error of random features regression.
method Performing ridge regression on N random features of the form σ(wa^T x), where wa are random weights.
result The test error follows a double descent curve, with a global minimum above the interpolation threshold.
STAT-SVD method reduces high-dimensional data sparsity, achieving optimal estimation.
problem Sparse tensor singular value decomposition for high-dimensional data.
method STAT-SVD method with double projection & thresholding scheme.
result STAT-SVD provides sharp thresholding criterion and minimax rate-optimal estimation.
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
Unified framework for solving low-rank plus sparse matrix recovery problems.
problem Solving general low-rank plus sparse matrix recovery problems.
method Unified framework based on matrix factorization, projected gradient descent, and double thresholding operator.
result Our algorithm converges to the unknown low-rank and sparse matrices at a locally linear rate, matching robustness guarantees.
Double descent observed in tree-based models for genomic prediction.
problem Understanding the generalization behavior of tree-based models in machine learning.
method Systematic variation of model complexity in a genomic prediction task using whole-genome sequencing data.
result Double descent emerges only when complexity is scaled jointly across learner capacity and ensemble size.
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
Analyzes double descent in binary classification models with different losses.
problem Understanding the double descent phenomenon in binary classification models.
method Analytic study of gradient descent with logistic and square losses on binary linear classification models.
result The double descent phenomenon persists but with differences compared to logistic loss.
Study on ridge regression in convolutional models shows double descent error behavior.
problem Understanding generalization and estimation error in over-parameterized convolutional models.
method Analysis of ridge estimators for convolutional linear models, derivation of exact error formulae.
result Ridge estimators exhibit double descent error behavior in high-dimensional convolutional models.
Study investigates overparametrization in survival models, revealing complex loss behavior.
problem Understanding overparametrization in survival models through interpolation.
method Defined interpolation and finite-norm interpolation, rigorously analyzed four survival models.
result Overparametrization can lead to improved performance in survival models, contrary to classical learning theory.
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
The paper explores cost-aware spectrum access strategies in cognitive radio systems.
problem Optimizing spectrum usage in cognitive radio systems with uncertain channel states and costs.
method Discrete time model with sensing and transmission phases, considering random costs and rewards.
result The optimal policy for spectrum access has a recursive double threshold structure, and online algorithms achieve near-optimal performance.
Power spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) for periods from January 1999 to December 2000 are analyzed. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and …
We calculate moments of decision times for diffusion models.
problem Modeling decision times in cognitive tasks.
method Derive expressions for the first three moments of decision times.
result Explicit formulae for third and higher moments are provided.
Revisits fuzzy neural networks with generalized Hamming distance, simplifying BN and ReLU.
problem Improving neural network techniques using fuzzy logic and generalized Hamming distance.
method Introducing generalized Hamming distance to reinterpret BN and ReLU, proposing GHN.
result Batch normalization and ReLU can be simplified or removed without loss of performance.
Model shows loss curve with two distinct exponents due to sparse activations.
problem Sparse activations impact neural network scaling laws.
method Introduced a model for neural scaling laws under sparse activations, derived asymptotic population loss, and analyzed gradient-descent dynamics.
result Loss curve exhibits double-descent peak near interpolation threshold with two distinct scaling exponents.
Overparameterization aids in model pruning, leading to improved test accuracy.
problem Improving lightweight model performance through pruning.
method Theoretical analysis and high-dimensional asymptotics of model pruning in overparameterized neural networks.
result Even with known informative features, training a large model and then pruning leads to better test accuracy.
Loyal buyer-seller relationships can arise by design, e.g. when a seller tailors a product to a specific market niche to accomplish the best possible returns, and buyers respond to the dedicated efforts the seller makes to meet their needs. We ask whether it is possible, instead, for loyalty to arise spontaneously, and…
The paper explores how noise in features can lead to benign overfitting in machine learning models.
problem Understanding the conditions for benign overfitting in machine learning models.
method Examined random feature models, specifically two-layer neural networks with fixed first layer weights, and analyzed the role of noise in features.
result Noise in features plays an important implicit regularization role in the phenomenon of benign overfitting.
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.
Neural networks generalize well despite overfitting due to high capacity.
problem Understanding why deep neural networks generalize well in overparameterized settings.
method High-dimensional asymptotic analysis of generalization under kernel regression with Neural Tangent Kernel.
result Test error exhibits non-monotonic behavior and can have additional peaks and descents in the overparameterized regime.
Developed a cost and revenue model for HEMS to estimate breakeven transport volumes under different reimbursement and labor cost assumptions.
problem Estimating breakeven transport volumes for HEMS under varying reimbursement and labor cost assumptions.
method Developed a two-part model: cost framework and actuarial revenue model using healthcare encounter data and payer reimbursement rates.
result Estimated breakeven transport volumes under different reimbursement and labor cost assumptions.
Develops ML tool for macroeconomic forecasting with clear interpretations.
problem Forecasting and understanding macroeconomic parameters over time.
method Macroeconomic Random Forest (MRF) algorithm, Generalized Time-Varying Parameters (GTVPs).
result Clear forecasting gains and accurate predictions of unemployment and inflation.
Optimal iterative thresholding algorithms improve upon hard and soft thresholding.
problem Optimizing sparsity or rank constraints in optimization problems.
method Developed the notion of relative concavity for thresholding operators, finding a new class of operators that are optimal.
result A new class of thresholding operators, including ℓq thresholding and reciprocal thresholding, achieves the strongest convergence guarantee. Deep linear networks oscillate beyond the edge of stability in a predictable manner.
problem Understanding oscillations in deep linear networks beyond the edge of stability.
method Theoretical analysis of loss oscillations in deep matrix factorization loss.
result Loss oscillations in deep linear networks follow a period-doubling route to chaos and occur within a small subspace.
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface X is a Klein surface Y such that there is a degree two morphism (of Klein surfaces) Y→X. There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the …
Defines double principal bundles with applications in geometry.
problem Understanding structures in double vector bundles.
method Definition and analysis of double principal bundles.
result Double vector bundles can be realized as associated bundles of their frame bundles.
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (…
We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct i…
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
The word `double' was used by Ehresmann to mean `an object X in the category of all X'. Double categories, double groupoids and double vector bundles are instances, but the notion of Lie algebroid cannot readily be doubled in the Ehresmann sense, since a Lie algebroid bracket cannot be defined diagrammatically. In this…
Algorithm solves online binary classification and infinite games using ERM oracle.
problem Online learning and solving infinite games with computationally inefficient oracles.
method Proposes an algorithm relying solely on ERM oracle calls for online binary classification and nonparametric games.
result Achieves finite and sublinearly growing regret in various settings.
Generalizes Hecke algebra for double torus, linking to skein algebra.
problem Understanding algebraic structures on double torus.
method Introducing Heegaard dual operators and Dehn twists.
result Established relationship between Hecke algebra and skein algebra.
Introduces Poisson double algebroids and their relation to Lie 2-bialgebras.
problem Developing Lie theory for Poisson double structures.
method Introducing Poisson double algebroids and double Lie bialgebroids, and relating them through differentiation and integration.
result Revisits Lie 2-bialgebras using Poisson double structures.
Survey of global geometry for double field theory.
problem Global description of double field theory geometry.
method Review of Courant algebroids, metric algebroids, AKSZ construction, para-Hermitian geometry.
result Global description of doubled geometry and topological models.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
Criteria found for knots not determined by their double branched covers.
problem Determining knots from their double branched covers.
method Criteria based on tunnel number one knots and their double branched covers.
result Provided criteria for knots not determined by their double branched covers.
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and various iterated tangent/cotangent constructions in symplectic and Poisson geometry…
Paper proposes a method to identify optimal threshold for stock market networks.
problem Challenges in identifying the optimal threshold for reliable stock network construction.
method Dynamic consistence between threshold network and stock market, optimal threshold maximized by consistence function.
result Optimal threshold value of 0.28 for stocks in S&P 500 Index.
We develop new algebraic methods refining the Witt group of linking forms and Ranicki's torsion algebraic L-groups into double Witt groups and double L-groups. At each prime ideal of the underlying ring, our double Witt groups capture infinitely many more integral signatures of the linking form than the single Witt gro…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation and basic examples come from Analytical Mechanics, where double affine bundles hav…
Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
problem Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
method Perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen-vectors of the ambient Ricci tensor, with general multiplicity results via Lusternik-Schnirelman theory.
result Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
We show that if K is any knot whose Ozsvath-Szabo concordance invariant tau(K) is positive, the all-positive Whitehead double of any iterated Bing double of K is topologically but not smoothly slice. We also show that the all-positive Whitehead double of any iterated Bing double of the Hopf link (e.g., the all-positive…