arXiv research

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

New equivalences found between subsampling and ridge regularization methods.

Improved bound for optimal Moebius band aspect ratio.

Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized. Mathematically, success …

Gradient descent dynamics in nonconvex models explained with universality.

Study optimal ridge regularization for out-of-distribution prediction.

Optimizes kernel density ratios for better predictions and information measures.

Noise increases the Rashomon ratio, leading simpler models to perform similarly to complex ones.

Paper introduces lexical ratio to measure portfolio diversification.

Aggregation defenses improve deep learning models' robustness against data poisoning attacks.

We prove that for every smooth Jordan curve $γ$, if $X$ is the set of all $r \in [0,1]$ so that there is an inscribed rectangle in $γ$ of aspect ratio $\tan(r\cdot π/4)$, then the Lebesgue measure of $X$ is at least $1/3$. To do this, we study sets of disjoint homologically nontrivial projective planes smoothly embedde…

We present an elementary analysis of the dynamical aspects of the GDP / government surplus multiplier with relevance to the assessment of a country's debt repayment policy. We show the (at first) counter intuitive result that in order to reduce the Debt/GDP ratio, countries with high Debt to GDP should go into further …

Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We develop the multicomponent functionalized Cahn-Hilliard (mFCH) free…

As deep neural networks (DNNs) achieve tremendous success across many application domains, researchers tried to explore in many aspects on why they generalize well. In this paper, we provide a novel perspective on these issues using the gradient signal to noise ratio (GSNR) of parameters during training process of DNNs…

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captur…

The paper analyzes the benefit-cost ratio for feature selection in machine learning.

Framework mitigates risk non-monotonicity in high-dimensional predictions.

We present a reinforcement learning approach for detecting objects within an image. Our approach performs a step-wise deformation of a bounding box with the goal of tightly framing the object. It uses a hierarchical tree-like representation of predefined region candidates, which the agent can zoom in on. This reduces t…

Solves constant pre-factor problem for tt*-Toda equations using asymptotic data and symplectic structures.

It had been believed in the conventional practice that the risk of a bank going bankrupt is lessened in a straightforward manner by transferring the risk of loan defaults. But the failure of American International Group in 2008 posed a more complex aspect of financial contagion. This study presents an extension of the …

In this paper, we propose a novel learning method for image classification called Between-Class learning (BC learning). We generate between-class images by mixing two images belonging to different classes with a random ratio. We then input the mixed image to the model and train the model to output the mixing ratio. BC …

New algorithm for MDS with quasi-polynomial dependency on aspect ratio.

Data augmentations are important ingredients in the recipe for training robust neural networks, especially in computer vision. A fundamental question is whether neural network features encode data augmentation transformations. To answer this question, we introduce a systematic approach to investigate which layers of ne…

Optimal ridge regularization computed iteratively from generative parameters.

PolyModel theory and iTransformer improve hedge fund portfolio construction.

Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.

DeepCTRL integrates rules into deep learning models, allowing flexible control at inference.

The book explains deep learning theory and how networks learn nontrivial representations.

Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.

Paper proposes new strategies for better portfolio estimation in long-term investments with unknown distributions.

FS-GCLSTM predicts stock returns by leveraging value-chain relationships.

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 …

This paper categorizes and analyzes existing outlying aspect mining methods.

Researchers validate ML scenario generators by checking dependencies and detecting memorization effects.

MSTREAM detects anomalies in multi-aspect data streams.

The paper proposes an asset allocation strategy using the Sortino ratio for better performance.

Featurization improves density ratio estimation for complex data.

The paper proposes using density ratio estimation to evaluate synthetic data quality.

This study argues for pruning trees in random forests to improve performance in low signal-to-noise scenarios.

Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe fail to capture some crucial aspects due to the strong non-Gaussian character of He…

Optimal data split ratio is sqrt(p):1 for linear regression.

Proposes a method to cluster multi-aspect data using manifold learning with NMF.

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…

Proposes a robust method for predicting missing outcomes in covariate shift adaptation.

New financial ratios using compositional data improve analysis of firm health.

New approach for algorithms that learn predictors to improve performance.

Neural networks approximate likelihood ratios for complex models.

Flow preserves isoperimetric ratio for immersed surfaces.