A universal LSTM model outperforms asset-specific models in forecasting stock volatilities.
problem Forecasting stock volatilities across different assets.
method Trained an LSTM network on a pooled dataset of liquid stocks to forecast daily realized volatilities.
result The LSTM model consistently outperforms other asset-specific parametric models in volatility forecasting.
This paper proposes efficient parametrization of deep neural networks for multiple domains.
problem Limitation of deep neural networks to a single task and visual domain.
method Universal parametric families of neural networks, differing only by a small number of parameters.
result Universal parametrization yields higher compression and outperforms traditional fine-tuning techniques in transfer learning.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
problem Proving the universality of CFlows in approximating diffeomorphisms.
method Deriving the universality of Para-CFlows through affine coupling layers and invertible linear transforms.
result Para-CFlows can approximate any diffeomorphism in C^k-norm.
Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is. For practical use, such a measure should be universal in the sense that it capt…
We analyze the constituents stocks of the Dow Jones Industrial Average (DJIA30) and the Standard & Poor's 100 index (S&P100) of the NYSE stock exchange market. Surprisingly, we discover the data collapse of the histograms of the DJIA30 price fluctuations and of the S&P100 price fluctuations to the universal non-paramet…
DebiNet uses over-parameterized neural networks to improve linear model performance and debiasing.
problem Improving linear model performance and debiasing in high-dimensional settings.
method Incorporates over-parameterized neural networks into semi-parametric models to estimate parameters consistently.
result DebiNet offers valid inference and accurate prediction by leveraging neural networks' universal approximation and linear model's interpretability.
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we pr…
Physics-informed neural networks and neural operators speed up solving parametric PDEs by orders of magnitude.
problem Solving PDEs for varying parameters is computationally expensive.
method Physics-informed neural networks and neural operators learn solution mappings across parameter spaces.
result Neural operators achieve computational speedups of 10^3 to 10^5 times faster than traditional methods.
New method tests independence in time series data.
problem Testing independence between time series data.
method Temporal dependence statistic with block permutation.
result Asymptotically valid and universally consistent test for independence.
We give an explicit local formula for any formal deformation quantization, with separation of variables, on a Kähler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.
The study characterizes quasiperiodic surfaces in pseudo-hyperbolic spaces with curvature conditions.
problem Characterizing quasiperiodic surfaces in pseudo-hyperbolic spaces.
method Curvature conditions, Gromov hyperbolicity, conformal hyperbolicity.
result Limit curves of quasiperiodic surfaces in the Einstein Universe have canonical quasisymmetric parametrizations.
Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.
problem Global optimality of extremal trajectories in a series of Lorentzian structures.
method Analysis of a one-parametric series of left-invariant Lorentzian structures on SL(2,R) with SO(1,1) symmetry.
result Properties of the Lorentzian structures deform to those of the sub-Lorentzian structure in a limit case.
Proposes a new parametric thresholding algorithm for NP classification without requiring minimum sample size on class 0.
problem Achieving minimal type II error while controlling type I error in binary classification, especially in rare disease diagnosis.
method Employed parametric linear discriminant analysis (LDA) and proposed a new thresholding algorithm.
result Proves NP oracle inequalities for one classifier, benefiting from explicit parametric model assumption.
Neural-Kernelized method estimates conditional densities without parametric assumptions.
problem Estimating conditional densities on large datasets with neural networks.
method Score matching with neural networks and neural-kernelized approach.
result Consistent in conditional density estimation, compares favorably with existing methods.
A universal collection of 4 invariants improves neural network accuracy for molecular dynamics.
problem Improving accuracy of neural networks in molecular dynamics.
method Developed a universal collection of 4 smooth scalar invariants on M(3) x M(3) and evaluated their effectiveness in a PONITA neural network architecture.
result Using a universal collection of invariants significantly improves neural network accuracy.
We propose using category theory to unify deep learning architectures.
problem Lack of a coherent bridge between model constraints and implementations.
method Apply category theory to unify neural network design.
result Theory recovers constraints from geometric deep learning and encodes standard constructs.
Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
New approach to linear regression using universal learning.
problem Applying universal learning to linear regression.
method Using a Gaussian error hypothesis class and Predictive Normalized Maximum Likelihood (pNML) solution.
result Linear regression can generalize even with over-parametrized models under certain conditions.
The paper addresses the gap between theoretical and practical confidence set widths in universal inference.
problem Inference procedures can be overly conservative, leading to wider confidence sets than expected.
method The authors identify the source of asymptotic conservativeness and propose a remedy based on studentization and bias correction.
result The proposed method achieves exact asymptotic coverage at the nominal 1−α level, even under model misspecification. Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
New model analyzes dynamic correlations in stock returns.
problem Analyzing time-varying correlations in high-dimensional data.
method Dynamic factor correlation model with novel parametrization.
result Model accurately captures heterogeneous heavy-tailed distributions and dependent shocks.
A universal method for hypothesis tests and confidence sets without regularity conditions.
problem Difficult inference in irregular statistical models.
method Modified likelihood ratio statistic (split LRT).
result Works for any parametric and some nonparametric models.
New law explains why deep learning models often have more parameters than needed.
problem Why deep learning models often have more parameters than classical theory suggests.
method Proved a universal law of robustness for smooth interpolation.
result Smooth interpolation requires d times more parameters than mere interpolation.
A new method forecasts financial tail risks by combining and weighting quantiles.
problem Reducing uncertainty in financial tail risk forecasting.
method Two-step procedure: quantile combination followed by ES computation.
result The proposed framework outperforms individual models and simple approaches.
Together with the Moebius strip, the Klein bottle is one of the intriguing objects in the universe of geometry, sometimes appearing in non-mathematical contexts too. Until now, several parametrizations of it as a surface immersed in ordinary three-space have been found, some of which are very elegant and lead to nice a…
We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the so-called (H,q)-derivative is applied to seven time series ending with the October 1987…
Study shows limitations and universality of equivariant QNNs with Sn-equivariant gates.
problem Understanding the expressiveness of Sn-equivariant QNNs with k-body gates. method Investigated the interplay between symmetry and k-bodyness in Sn-equivariant QNN generators. result QNNs are semi-universal but not universal with one- and two-body Sn-equivariant gates. Deep neural networks without regularization can achieve consistent estimates with good convergence rates.
problem The necessity of regularization in deep neural networks for consistent estimates.
method Gradient descent on an over-parametrized neural network without regularization, with specific initialization, step size, and number of steps.
result An estimate without regularization is universally consistent and achieves good convergence rates.
New framework predicts crypto volatility, outperforming traditional models.
problem Forecasting volatility in cryptocurrencies during the crypto-winter.
method Combines LSTM and rough volatility models, using a parsimonious parametric model.
result Similar prediction performances with fewer parameters, suggesting universality of volatility mechanisms.
A new machine-learned CG model predicts protein structures efficiently.
problem Developing a universal, computationally efficient protein simulation model.
method Combining deep learning with all-atom protein simulations to create a transferable CG force field.
result The model predicts protein structures, intermediates, and fluctuations efficiently.
OptiNet achieves near-minimax error rates with compression in Euclidean space.
problem Error and compression rates in non-parametric multiclass classification.
method Compression-based learning rule OptiNet and a novel general compression scheme.
result OptiNet achieves non-trivial compression rates with near-minimax error rates in Euclidean space.
Paper analyzes localized SVMs for robustness and consistency.
problem Handling large datasets efficiently and robustly.
method Localized support vector machines (SVMs) for non-parametric learning.
result Locally learnt kernel methods are universal consistent and robust.
New criterion selects optimal number of clusters based on stability.
problem Challenges in selecting optimal number of clusters in non-parametric clustering.
method Proposes a stability-based validation criterion combining between-cluster and within-cluster stability.
result Empirically demonstrates effectiveness in selecting optimal number of clusters.
Proposes a non-parametric method to calibrate classifier confidence estimates.
problem Inaccurate uncertainty estimation in classification methods.
method Uses a latent Gaussian process for non-parametric calibration of any classifier.
result Improves calibration of confidence estimates across various classifiers and datasets.
Study of pluriclosed flow on Oeljeklaus-Toma manifolds, showing convergence to a soliton.
problem Investigating the behavior of pluriclosed flow on Oeljeklaus-Toma manifolds.
method Parametrized left-invariant pluriclosed metrics, classified, and analyzed the flow's long-time behavior.
result The flow converges to an algebraic soliton, with normalized metrics collapsing to a torus.
New kernel class improves SVM performance.
problem No universal, tractable, scalable kernel set.
method Proposed Tessellated Kernel (TK) class with positive matrices.
result TK kernels outperform other methods in SVM problems.
A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. We perform an empirical analysis of a recent, high-quality data set from a large electronic tra…
USFAs combine UVFAs, SFs, and GPI for scalable, instant RL generalisation.
problem Generalizing to unseen tasks in reinforcement learning.
method Combining universal value function approximators, successor features, and generalized policy improvement.
result Demonstrates practical benefits and transfer abilities in a complex 3D environment.
New method calibrates MQHawkes model using non-parametric approach, identifying cross-Hawkes and cross-leverage effects.
problem Calibrating complex Hawkes processes with non-parametric methods.
method Non-parametric calibration using General Method of Moments on coarse-grained MQHawkes model.
result Identification of cross-Hawkes and cross-leverage effects in futures markets.
A classical result of Sampson and Schoen-Yau in 1978 states that every diffeomorphism between compact hyperbolic Riemann surfaces is homotopic to an harmonic diffeomorphism. As conjectured by Schoen in 1993 and partially proved by Wan in 1992 and Tam-Wan in 1995, we prove in this article that this theorem generalizes t…
Interpolation improves performance in nearest neighbor algorithms without over-parametrization.
problem Achieving zero training error in deep learning without over-parametrization.
method Introduced a class of interpolated weighting schemes in nearest neighbor algorithms.
result Mild data interpolation strictly improves prediction performance and statistical stability.
Constructs Higgs bundle moduli spaces using Teichmüller space.
problem Holomorphic family of Higgs bundle moduli spaces over a curve.
method Uses a function f on the character variety to define flat Ehresmann connections.
result Reveals various aspects of moduli spaces and their metrics.
Paper proposes a novel auto-encoder for latent density estimation.
problem Challenges of learning generative probabilistic models due to curse of dimensionality.
method Joint dimensionality reduction and non-parametric density estimation framework using a novel estimator.
result Proposed model achieves promising results on various datasets.
Let M a compact connected orientable 4-manifold. We study the space Ξ of Spinc-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M. In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of…
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
The book explores universal time-series forecasting using mixture predictors.
problem Sequential probability forecasting in a general setting.
method Mixture predictors combining multiple predictors.
result Universality of mixture predictors in a general probabilistic setting.
Paper proposes Nyström sketches for better adaptive compressive learning.
problem Improving adaptability of sketching for compressive learning.
method Data-dependent Nyström approximation for mean embedding.
result Excess risk can be controlled with geometric assumption.