arXiv research

Study shows overparametrization can shift and bend loss landscapes, affecting signal recovery.

Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.

Consistent model selection for spiked Wigner model via AIC-type criteria.

Optimal spectral method found for inhomogeneous spiked Wigner model.

Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.

We apply a local differential geometric framework from Kähler toric geometry to (re)construct Calabi's extremal Kähler metrics on $\bbC\bbP^n$ blown-up at a point from data on the moment polytope.

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

Study of correlated Wigner matrices with BBP transitions.

New method detects global factors near BBP phase transition in high-dimensional data.

Study reveals limits of PLS in multi-modal learning with correlated signals.

PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a qu…

Random matrix theory explains transient signal detectability in early-stopped gradient flow.

Study on signal recovery from low-rank matrix with sparse noise.

Improves detection of low-rank signals from noisy data matrices.

Gradient flow in phase retrieval escapes spurious minima with high probability.

We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This setup includes Johnstone's spiked covariance model. We analyze the likelihood ratio …

RBM learns in high dimensions via AMP and GD, reaching optimal weak recovery.

New algorithm achieves optimal clustering for sparse centers with high dimensions.

Randomized SVD shows phase transitions in noisy data.

Study reveals how attention helps in signal recovery from sequence models using random matrix theory.

Improves signal detection in non-Gaussian noise using transformed data.

Holomorphic splitting theorem for Calabi-Yau manifolds with specific properties.

Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it i…

Developed a new thresholding method that connects soft and hard thresholding.

We consider a stochastic volatility model with Lévy jumps for a log-return process $Z=(Z_{t})_{t\geq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{t\geq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{t\geq 0}$ is an independent Lévy process with absolutely continuous Lévy measure $ν$. Small-time expansio…

New algorithm for reinforcement learning in uncertain environments with unknown thresholds.

A new SSL method uses instance-dependent thresholds to improve accuracy.

Study stability thresholds of big line bundles, proving bounds and generalizing results.

Adaptive algorithm for outlier detection by balancing arm exploration and threshold estimation.

In this paper we studied about the wavelet identification of the thresholds and time delay for more general case without the constraint that the time delay is smaller than the order of the model. Here we composed an empirical wavelet from the SETAR (Self-Exciting Threshold Autoregressive) model and identified the thres…

The article examines different thresholding methods for improving PAM algorithm in cancer classification.

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…

Although the threshold network is one of the most used tools to characterize the underlying structure of a stock market, the identification of the optimal threshold to construct a reliable stock network remains challenging. In this paper, the concept of dynamic consistence between the threshold network and the stock ma…

Proposes a conservative LR estimator for infrequent data near a frequency threshold.

New method trains neural networks with threshold activation functions efficiently.

Noise makes learning linear thresholds hard, but algorithms can still learn near-optimal thresholds.

Bayesian framework proves thresholds for multi-graph alignment feasibility.

Polynomial neural networks explore thresholds for maximum expressiveness.

Paper introduces threshold invariant fairness to ensure equitable predictions across different groups.

Study evaluates thresholds for removing noise from DNN weights using random matrix theory.

FILTER model uses fusion penalized logistic threshold regression for high-dimensional data with unknown cut points.

New analysis reveals masked self-supervised learning's effectiveness in extracting data structure.

The paper considers an investment timing problem appearing in real options theory. Present values from an investment project are modeled by general diffusion process. We prove necessary and sufficient conditions under which an optimal investment time is induced by threshold strategy. We study also the conditions of opt…

Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.

A new algorithm infers causal networks from data using topological thresholds.

In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We use the expected number of jump misclassifications as the objective function to…

Study on discrete Okounkov bodies and their applications.