arXiv research

Deep networks can approximate functions with fewer learnable parameters than previously thought.

Improves generalization in learning problems with small parameter method.

Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…

Small Nijenhuis tensor found on compact manifolds.

Estimates matrix trace optimization with statistical learning theory.

The study bounds the stability of Gaussian mixtures under small perturbations.

We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…

Study small eigenvalues of Riemann surfaces degenerating with Kähler metrics.

Study on colored Jones polynomial of figure-eight knot for complex parameters.

New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.

We prove uniqueness of solutions to complex Monge-Ampère equations for small temperature.

Deep neural network solves portfolio optimization with MGARCH and small transaction costs.

We compare communication efficiencies of two compelling distributed machine learning approaches of split learning and federated learning. We show useful settings under which each method outperforms the other in terms of communication efficiency. We consider various practical scenarios of distributed learning setup and …

A scalable method for Bayesian inference in large linear models.

The growing use of Machine Learning has produced significant advances in many fields. For image-based tasks, however, the use of deep learning remains challenging in small datasets. In this article, we review, evaluate and compare the current state-of-the-art techniques in training neural networks to elucidate which te…

Novel approach for SEM in small samples with $p>n$.

Study small eigenvalues of Toeplitz operators and their relation to Mabuchi geodesics.

Deep Neural Networks (DNNs) are usually over-parameterized, causing excessive memory and interconnection cost on the hardware platform. Existing pruning approaches remove secondary parameters at the end of training to reduce the model size; but without exploiting the intrinsic network property, they still require the f…

Simulation reveals relationships in stock market pyramid schemes.

This note provides an elementary proof of the folklore fact that draws from a Dirichlet distribution (with parameters less than 1) are typically sparse (most coordinates are small).

S$^2$GPT-PINNs solve PDEs with sparse, small models.

Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model $N$ times for a dataset of size $N$. Previous work has shown that approximations to LOOCV…

SHADOWCAST generates graphs with user-specified attributes.

Training large and highly accurate deep learning (DL) models is computationally costly. This cost is in great part due to the excessive number of trained parameters, which are well-known to be redundant and compressible for the execution phase. This paper proposes a novel transformation which changes the topology of th…

Deep learning (DL) training-as-a-service (TaaS) is an important emerging industrial workload. The unique challenge of TaaS is that it must satisfy a wide range of customers who have no experience and resources to tune DL hyper-parameters, and meticulous tuning for each user's dataset is prohibitively expensive. Therefo…

A new method uses recurrent nets to efficiently estimate SEIR model parameters.

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves' travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators obtained from the pseudolinearization argument are of parabolic type, and so we dis…

We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both $β$ parameters equal to $1$ and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on …

Deep learning used for parameter estimation in hard-to-infer models.

Study small eigenvalues on Kähler manifolds degenerating with induced metrics.

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stocha…

PPI++ uses machine learning predictions to improve inference from small datasets.

We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transf…

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular networks with a learnt structure can generalise better on small datasets, while f…

Simple private estimators for mean and covariance outperform existing methods.

Study develops a method to select penalty parameters for sparse neural networks without cross-validation.

An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. Thes…

We improve robust parameter estimation in causal models from observational data.

The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient pr…

The cold posterior effect is explored through PAC-Bayes bounds for small sample sizes.

We propose CAVIA for meta-learning, a simple extension to MAML that is less prone to meta-overfitting, easier to parallelise, and more interpretable. CAVIA partitions the model parameters into two parts: context parameters that serve as additional input to the model and are adapted on individual tasks, and shared param…

Paper optimizes neural network initialization using SMT solvers.

New method improves nonlinear filtering accuracy with reduced computation.

CDEFs reduce model complexity and uncover time correlations.

Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.

Two algorithms for linear contextual bandits with rare updates achieve optimal regret and efficiency.

In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a convolutional filter can be well approximated as a linear combination of a small set of dict…

Proposes a deep learning method for modeling dynamic individual-level latent trajectories with changing parameters.