Proposes first method for continuously indexed domain adaptation.
problem Challenges of transferring knowledge between continuously indexed domains.
method Combines adversarial adaptation with a novel discriminator.
result Outperforms state-of-the-art methods on synthetic and real-world datasets.
New methods estimate probabilities from pairwise comparisons, adapting to difficulty.
problem Estimating probabilities from pairwise comparisons with varying difficulty.
method Adaptive estimators using an adaptivity index based on indifference sets.
result CRL estimator has adaptivity index upper bounded by n \sqrt{n} n up to logarithmic factors. Adaptive framework improves NB accuracy by fusing two index categories.
problem Challenges in attribute weighted NB, especially fusion of two indexes.
method Proposes ATFNB framework using switching factor to fuse two index categories.
result ATFNB outperforms basic NB and state-of-the-art models.
Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.
problem Adaptive contextual bandits with single-index models and unknown link functions.
method Kernelized ε-greedy algorithm combining Stein-based index estimation and kernel ridge regression for reward functions.
result Unified framework for simultaneous learning and inference in single-index contextual bandits.
Paper adapts Getzler's grading technique for new applications.
problem Computing leading terms of asymptotic expansions of traces of heat kernels.
method Adapting Getzler's grading technique to two new contexts.
result Adapted technique yields leading terms of asymptotic expansions.
The paper proves continuity of Morse index for Ricci shrinkers.
problem Lower and upper semi-continuity of the Morse index for gradient Ricci shrinkers.
method Adapting and refining recent arguments on CMC hypersurfaces and polynomially weighted Sobolev spaces, with techniques for non-compact shrinkers.
result Identifies a condition ensuring the Morse index of asymptotically conical shrinkers is bounded below by the f-index of their asymptotic cone.
Local EGOP learns functions varying along a few directions.
problem Efficient estimation of functions varying along a few directions in high-dimensional space.
method Local EGOP learning, a recursive algorithm using EGOP quadratic form as metric and inverse-covariance.
result Local EGOP learning achieves intrinsic dimensional learning rates under noisy manifold hypothesis.
Adapts robust risk measures to spectral measures and quantifies uncertainty.
problem Risk assessment under uncertain scenarios leading to financial losses.
method Adapts robust framework to spectral risk measures and proposes a Deviation-based approach.
result Illustrates practical case study from NASDAQ index.
Estimates the growth of Morse index for free boundary minimal hypersurfaces.
problem Estimating the Morse index of free boundary minimal hypersurfaces.
method Adapting Song's method to the free boundary case.
result The Morse index grows linearly with the sum of Betti numbers.
Researchers compute the index of a specific operator on contact manifolds.
problem Computing the index of a twisted Dolbeault operator on toric contact manifolds.
method Using equivariant techniques, they localized the symbol to Reeb orbits and applied polytope decomposition.
result They derived an Atiyah-Bott-Lefschetz type formula for the index.
Adaptive Heston model calibration using PCRLB and switching filters.
problem Estimating volatility in stochastic volatility models like Heston.
method Bayesian filtering (EKF, UKF, PF) with PCRLB for parameter estimation.
result Adaptive estimation of Heston model parameters improves volatility estimation.
We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for th…
Paper improves Morse index bound for hypersurfaces.
problem Improving Morse index bound for hypersurfaces.
method Construction of hierarchical deformations and restrictive min-max theory.
result Generalizes a result by X. Zhou for 3 ≤ n + 1 ≤ 7 3 \leq n+1 \leq 7 3 ≤ n + 1 ≤ 7 . A blockchain protocol uses bandit algorithms to dynamically price transactions.
problem Maximizing revenue from decentralized blockchain Indexers competing for queries.
method Dynamic pricing using Gaussian bandits for multiple agents.
result Improved revenue through dynamic pricing in a decentralized blockchain environment.
We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf closures. The primary tool used to establish this result is an adaptation to foliati…
Method improves volatility targeting for index construction.
problem High turnover, leverage spikes, and sensitivity to estimation error in existing volatility-targeting strategies.
method Proportional-control approach for setting index weights that corrects tracking error through feedback.
result The proportional-control approach achieves the target volatility more effectively than open-loop alternatives.
This paper extends the single index model to handle nonlinear relationships.
problem Nonlinear relationships in regression models.
method Exploits conditional distribution over function-driven partitions and uses linear regression for local estimation of index vectors.
result The method provides theoretical guarantees for estimation and prediction, and outperforms state-of-the-art methods.
Adaptive learning model forecasts financial prices using order book data.
problem Forecasting high-frequency financial time series with non-stationary data.
method Adaptive learning model based on order book data, with stationarity and non-stationarity considerations.
result The model outperforms top fixed models and improves forecasting accuracy.
Proposes a transfer learning framework for sparse SIMs without raw source data.
problem Lack of direct access to raw source data and known link functions in transfer learning.
method Source-data-free framework based on SIM, using summary statistics and a multilayer perceptron.
result Consistent improvements over existing approaches in synthetic and real-world data.
Study finds varying market efficiency in prewar and wartime Japanese stock market.
problem Measuring market efficiency in prewar and wartime Japanese stock market.
method Using a new market capitalization-weighted stock price index, the study examines market efficiency over time and historical events.
result The adaptive market hypothesis is supported in the prewar and wartime Japanese stock market, with efficiency varying over time and with historical events.
SA-REMBO adapts to nonstationary high-dimensional optimization.
problem Bayesian Optimization in high-dimensional spaces is limited by the curse of dimensionality and rigidity of global assumptions.
method SA-REMBO uses multiple random Gaussian embeddings and an index variable to adaptively select the best embedding for the optimization problem.
result SA-REMBO outperforms traditional REMBO and other low-rank BO methods across synthetic and real-world benchmarks.
HKRR adapts to MIM, overcoming the curse of dimensionality.
problem Understanding when deep networks outperform kernel methods in high dimensions.
method Hyper-kernel ridge regression (HKRR) for multi-index models (MIM).
result HKRR can adaptively learn MIM, overcoming the curse of dimensionality.
We analyze bias in post-bandit inference for stable index algorithms.
problem Bias in post-bandit inference for stable index algorithms.
method Empirical fluid approximation of sampling dynamics.
result Sharp leading-order expressions for bias and expected Z-statistic.
Unified framework for AMP iterations using graph indexing.
problem Complex high-dimensional statistical inference problems.
method Graph-based indexing of AMP iterations, modular proof of state evolution.
result Unified SE equations for AMP iterations indexed by graphs.
Optimism stabilizes Thompson Sampling for adaptive inference in multi-armed bandits.
problem Subtle inferential properties of Thompson Sampling under adaptive data collection.
method Introduced optimism as a key mechanism to restore stability and validity of inference.
result Suitably implemented optimism stabilizes Thompson Sampling and enables asymptotically valid Wald inference.
SGD shows distinct phases in learning single-index models, achieving optimal sample complexity and regret.
problem Learning single-index models with SGD in adaptive data settings.
method Stochastic gradient descent (SGD) with an optimal learning rate schedule.
result SGD achieves near-optimal sample complexity and regret guarantees across both burn-in and learning phases.
Estimates isotonic functions under unknown permutations, achieving optimal statistical and computational efficiency.
problem Estimating isotonic functions with unknown permutations in multiway comparison data.
method Mirsky partition estimator for minimax optimal and adaptive estimation.
result Achieves optimal worst-case statistical performance and computational efficiency.
The paper extends cluster validity indices for incremental analysis.
problem Providing incremental alternatives for cluster validation.
method Extending iCVI family to include 6 incremental indices and examining their behavior under under- and over-partitioning.
result Over-partitioning is more challenging to detect than under-partitioning.
AGMMNs improve learning of copula models by adaptively selecting kernels.
problem Learning dependence structures in copula models.
method Adaptive bandwidth selection for MMD in GMMNs, increasing kernels based on validation loss.
result AGMMNs significantly improve training performance over GMMNs and parametric models.
The Knowledge Gradient policy is improved for MABs by avoiding dominated actions.
problem Weaknesses in KG policy for MABs, including taking dominated actions.
method Proposed variants of KG that avoid taking dominated actions, including an index heuristic.
result New policies perform well over a range of MABs, including those for which index policies are not optimal.
New neural networks learn single-index models efficiently.
problem Learning low-dimensional structure in high-dimensional data.
method Shallow neural networks with frozen biases, studied via gradient flow.
result Generalization guarantees match near-optimal sample complexity.
New CSIM index improves image patch recovery from missing data.
problem Recovering missing image samples using sparse representation.
method Proposes a new convex similarity index (CSIM) and an iterative sparse recovery method.
result Proves the convergence of the algorithm to the globally optimal solution.
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
New insights into SGD and SGD-M in high dimensions.
problem Understanding and comparing SGD and SGD-M in high-dimensional settings.
method Developed high-dimensional scaling limits for SGD-M and online SGD, examining their dynamics and performance.
result SGD-M amplifies high-dimensional effects, potentially degrading performance compared to online SGD.
New algorithm reduces regret in infinitely many-armed bandits with decreasing rewards.
problem Infinitely many-armed bandits with rotting rewards.
method UCB index and adaptive threshold for unknown rotting rate, UCB index alone for known rotting rate.
result Matching upper bounds on regret achieved for different scenarios.
AdaGrad converges under heavy-tailed noise without extra operations.
problem Optimizing with heavy-tailed noise in machine learning.
method Investigation of AdaGrad convergence under heavy-tailed noise.
result First provable convergence rate for AdaGrad in non-convex optimization.
Paper proposes Adaptive DDPG for better stock portfolio allocation.
problem Challenges in finding optimal stock portfolio allocation in dynamic stock markets.
method Adaptive Deep Deterministic Reinforcement Learning (Adaptive DDPG) incorporating optimistic or pessimistic reinforcement learning.
result Adaptive DDPG outperforms traditional and baseline strategies in investment return and Sharpe ratio.
Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle with connection on M. We define a coarse multi-partitioned index of the…
New spectral estimates for minimal surfaces with boundary conditions.
problem Quantifying the Morse index of free boundary minimal surfaces.
method Adapted Montiel-Ros partitioning methods to compact manifolds with boundary, accounting for mixed and group actions.
result Explicit two-sided linear bounds on the Morse index for minimal surfaces.
Supporting evidence for adaptive feature program across diverse models.
problem Analyzing feature learning in neural networks.
method Over-parameterized sequence models and feature error measure (FEM).
result FEM is decreasing during training of adaptive feature models.
New Morse theory techniques glue nontransverse flowlines.
problem Gluing nontransverse gradient flowlines in Morse theory.
method Adapted OBG techniques from Hutchings and Taubes to Morse theory.
result Explicit criteria for gluing certain flowlines.
Hybrid SA algorithm optimizes index tracking for large indices.
problem Optimizing index tracking for large indices with financial constraints.
method Hybrid simulated annealing algorithm.
result Algorithm finds optimal solutions for past and future returns.
Estimates translator stability via topological features.
problem Quantifying stability of translators in geometric flows.
method Adapted Li-Tam theory to weighted settings, estimating nullity of stability operator.
result Quantitative index bounds for translators via topology.
We study elliptic theory on manifolds with boundary represented as a covering space. Firstly, we consider boundary value problems, where the boundary conditions are allowed to mix the values of functions in the fibers of the covering. We show that elliptic elements define Fredholm operators and prove an index formula. …
TTT improves model adaptation to test data, especially for nonlinear models.
problem Improving model performance in adapting to test data, especially for nonlinear models.
method Combining Test-time Training (TTT) with In-context Learning (ICL) for nonlinear models.
result TTT enables models to adapt to both feature vector and link function shifts, improving performance.
New algorithm optimizes unimodal bandits using empirical divergence.
problem Optimizing decisions in multi-armed bandit problems with unimodal distributions.
method Indexed Minimum Empirical Divergence (IMED) adapted for unimodal structure.
result IMED-UB algorithm optimally exploits unimodal structure.
Geometric approach simplifies K-homology computation for Lie manifolds.
problem Computing the Fredholm index of fully elliptic operators on Lie manifolds.
method Adapting geometric K-homology concepts, introducing geometric cycles and a comparison map.
result Reduction of index computation to Dirac operator index with a smoothing operator.
The paper introduces a new model selection criterion for various time series models.
problem Designing adaptive model selection criteria for a wide range of time series models.
method The approach involves a penalized contrast akin to Hannan and Quinn's criterion, with a data-driven calibrated term.
result The new criteria select the true model almost surely asymptotically for a wide range of time series models.