arXiv research

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

Improved bound for optimal Moebius band aspect ratio.

New equivalences found between subsampling and ridge regularization methods.

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 …

Optimizes kernel density ratios for better predictions and information measures.

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…

Gradient descent dynamics in nonconvex models explained with universality.

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…

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

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…

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

Paper introduces lexical ratio to measure portfolio diversification.

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 …

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

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

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

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

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

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…

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

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

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…

New approach for algorithms that learn predictors to improve performance.

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 …

PolyModel theory and iTransformer improve hedge fund portfolio construction.

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we …

Paper tackles sparse recovery with shuffled labels, establishing statistical and computational limits.

We study two aspects of noisy computations during inference. The first aspect is how to mitigate their side effects for naturally trained deep learning systems. One of the motivations for looking into this problem is to reduce the high power cost of conventional computing of neural networks through the use of analog ne…

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

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 …

Paper explores limits of high-order clustering with planted structures.

Optimal ridge regularization computed iteratively from generative parameters.

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

The increasing illegal parking has become more and more serious. Nowadays the methods of detecting illegally parked vehicles are based on background segmentation. However, this method is weakly robust and sensitive to environment. Benefitting from deep learning, this paper proposes a novel illegal vehicle parking detec…

AB-testing is a very popular technique in web companies since it makes it possible to accurately predict the impact of a modification with the simplicity of a random split across users. One of the critical aspects of an AB-test is its duration and it is important to reliably compute confidence intervals associated with…

Paper optimizes ES estimation under an $\ell_1$ constraint, reducing estimation errors.

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

CNNs encode data augmentation transformations, especially in early layers.

The paper analyzes equity market dynamics and optimal portfolios using time-varying optimization.

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…

Study on quantitative aspects of trace polynomials in free groups.

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

asp2vec learns dynamic node aspect distributions for better network embedding.

We create a smooth manifold of triangular meshes with a geodesically complete metric.

Study on non-orientable surfaces and inscribed rectangles in 4-manifolds.

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