Global optimization in Bayesian inference yields little additional benefit.
problem Improving psychometric parameter estimation using global optimization strategies.
method Experimental simulations comparing myopic and global strategies in multiple models.
result Global optimization strategies provide negligible additional utility improvement beyond the immediate next steps.
A new Federated Learning approach balances personalization and global training.
problem Breaking the curse of data heterogeneity in Federated Learning.
method Splitting variables into global and local parameters, using a simple algorithm.
result The approach allows each client to fit their data perfectly, breaking the curse of data heterogeneity.
We prove that for every analytic curve in the complex plane, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Euc…
This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.
problem Estimating chaotic dynamics and parameters from observations.
method Local ensemble Kalman filters with covariance and local domain localisation.
result Rigorously updating global parameters using a local domain ensemble Kalman filter.
Gradient flow in parameters equals linear interpolation in outputs.
problem Understanding and optimizing training algorithms in deep learning.
method Proving equivalence between gradient flow in parameter space and linear interpolation in output space, and deriving formulas for global minima.
result Gradient flow in parameters can be transformed into linear interpolation in outputs, leading to global minima.
Constructs classifiers for neural networks with specific data configurations.
problem Finding global minima of deep ReLU neural networks on sequentially separable data.
method Explicitly constructs zero loss neural network classifiers using cumulative parameters and truncation maps.
result Global minimizers can be described with a limited number of parameters based on the data structure.
Federated learning algorithm reduces global model size by combining local and global representations.
problem Scalability issues in training large models on private data distributed over multiple devices.
method Proposes a federated learning algorithm that jointly learns compact local representations and a global model.
result The global model can be smaller since it only operates on local representations, reducing the number of communicated parameters.
Geodesic interpretation of global quasi-geostrophic equations on sphere.
problem Modeling dynamics on the sphere using geodesic equations.
method Interpreting equations as geodesic on central extension of quantomorphism group.
result Global-in-time existence and uniqueness of solutions with stabilizing Lamb parameter effect.
First order methods can take extremely long to find global minima of non-convex functions.
problem Finding global minimizers of non-convex functions.
method Designing a family of non-convex functions and using statistical lower bounds for parameter estimation.
result First order methods can take exponential time to converge to a global minimizer.
Gradient descent finds global optima in ResNets with sufficient parameters.
problem Finding optimal parameters in ResNet models.
method Mean-field analysis and gradient-flow PDE to study convergence of first-order optimization methods.
result First-order methods can find global minimizers in overparameterized ResNets.
Wide neural networks with asymmetrical node scaling converge globally and learn features.
problem Global convergence and feature learning in over-parameterised shallow networks.
method Gradient-based optimisation of wide, shallow neural networks with asymmetrical node scaling.
result Gradient flow and gradient descent converge to a global minimum and learn features, unlike in the NTK parameterisation.
HNPE uses auxiliary data to estimate parameters in uncertain models.
problem Uncertain models with identical observations.
method Exploits global parameters from auxiliary data to estimate parameters.
result Validated on a motivating example and applied to neuroscience.
A new method averages neural network parameters to rank features robustly.
problem Neural networks' sensitivity to random initialization affects feature ranking robustness.
method Parameter averaging of multiple shallow networks trained with different random seeds.
result The averaged model discovers ground-truth feature importance consistently.
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…
Improved global minimum-variance portfolios using cross-validation for high-dimensional covariance estimation.
problem Ill-conditioned sample covariance matrix in high-dimensional data leads to suboptimal portfolios.
method Cross-validation technique to select tuning parameters for efficient covariance matrix estimation methods.
result Data-driven tuning parameters improve out-of-sample performance of global minimum-variance portfolios.
Global minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
Proposes a differentially private bandit algorithm reducing noise over time.
problem Privacy concerns in interactive recommendation systems.
method Tree-based mechanism to add Laplace or Gaussian noise to model parameters, focusing on dynamic global sensitivity.
result Demonstrates (ε,δ)-differential privacy with reduced noise and improved regret. We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on l1- regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods di…
Climate projections suffer from uncertain equilibrium climate sensitivity. The reason behind this uncertainty is the resolution of global climate models, which is too coarse to resolve key processes such as clouds and convection. These processes are approximated using heuristics in a process called parameterization. Th…
Meta-analysis improves interpretation and efficiency across similar but non-identical datasets.
problem Meta-analysis of heterogeneous data in high dimensions.
method Integrative sparse regression with a global parameter for adaptability and anonymity.
result Superior identification of global parameter for high-dimensional linear models.
New algorithm trains deep neural networks without global optimization.
problem Training deep neural networks efficiently and without global optimization.
method Uses random complex exponential activation functions and Markov Chain Monte Carlo sampling.
result Consistently attains theoretical approximation rate for residual networks.
Gradient descent converges geometrically to optimal self-attention parameters.
problem Training softmax self-attention layers for linear regression.
method Structure-aware gradient descent with preconditioner and regularizer.
result Gradient descent converges geometrically to global minima.
Investigates maps and properties in spaces with negative dimensions and curvature.
problem Existence of transport maps and local-to-global property in spaces with negative dimensions and bounded Ricci curvature.
method Examines metric measure spaces with negative curvature dimensions and applies reduced curvature-dimension conditions.
result Establishes the existence of transport maps and proves the local-to-global property.
We present ARU, an Adaptive Recurrent Unit for streaming adaptation of deep globally trained time-series forecasting models. The ARU combines the advantages of learning complex data transformations across multiple time series from deep global models, with per-series localization offered by closed-form linear models. Un…
The paper proposes a new model for predicting and analyzing economic variables.
problem Predicting and analyzing economic variables in developed regions.
method Time-varying parameter global vector autoregressive (TVP-GVAR) framework combined with machine learning models.
result The proposed model provides high precision out-of-sample predictions and novel insights into economic variable connectedness.
New method improves uncertainty quantification in latent variable models.
problem Uncertainty quantification in latent variable models with SGLD-Gibbs.
method Statistical scaling limit theory for SGLD-Gibbs, proposing hyperparameter tuning.
result Explicit guidance on hyperparameter tuning for SGLD-Gibbs ensures meaningful uncertainty quantification.
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which guarantees the global consistency of distributed estimators, provided the local estimator…
We provide adaptive inference methods, based on ℓ1 regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular f…
Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.
problem Minimizing elastic bending energy for open planar curves with obstacles.
method Investigation of global minimizers and explicit solutions for different values of the penalization parameter.
result Explicit threshold for λ above which minimizers touch the obstacle, regardless of obstacle shape. Global compression method prunes deep neural networks efficiently.
problem Efficiently compress deep neural networks for resource-constrained devices.
method Global Sparse Momentum SGD for on-the-fly pruning.
result Automatically finds appropriate per-layer sparsity ratios without re-training.
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
Improved Bayesian FL method calibrates predictions for federated learning.
problem Overconfident predictions in Bayesian FL methods for federated learning.
method β-Predictive Bayes algorithm interpolates between mixture and product of local predictive posteriors, tuning parameter β for better calibration.
result Demonstrated superior calibration compared to other baselines, even with increased data heterogeneity.
The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.
problem Conditions for global smoothings of special Lagrangian submanifolds with isolated conical singularities.
method Proof of weaker conditions for global smoothings.
result Global smoothings are possible under weaker hypotheses than previously known.
New method bypasses global fit for LISA's Galactic binaries, extracting population parameters directly.
problem Disentangling LISA's Galactic binary sources from backgrounds in a computationally intensive process.
method Simulation-based approach using normalizing flow to infer population parameters.
result Direct inference of population parameters from LISA's frequency strain series.
Geometric operators link solutions on different spacetimes.
problem Comparing solutions on different globally hyperbolic manifolds.
method Intertwining operators preserving Hermitian forms.
result Existence of Hadamard states on globally hyperbolic manifolds.
Coded Federated Learning speeds up model convergence by preemptively computing on parity data.
problem Federated learning's convergence is slow on heterogeneous platforms due to stragglers.
method Develops CFL scheme where clients generate parity data and share it once, allowing the server to compute redundantly.
result CFL allows global model to converge nearly four times faster than uncoded federated learning.
Federated learning improves with adaptive hyper-parameters and representation matching.
problem Heterogeneous client data leads to divergent local models in federated learning.
method Representation matching and adaptive hyper-parameters.
result Significant performance and robustness improvements in federated learning.
Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scal…
The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.
problem Minimizing nonsmooth nonconvex functions with convergence guarantees.
method Developed a framework for stochastic subgradient methods with global stability guarantees.
result Iterates are uniformly bounded and asymptotically stabilize around the stable set of the differential inclusion.
Paper uses DFL to optimize portfolio risk and outperforms conventional methods.
problem Optimizing portfolio risk and return under uncertainty.
method Decision-focused learning (DFL) to derive global minimum variance portfolio (GMVP).
result DFL-based methods consistently deliver superior decision performance in portfolio optimization.
The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The convergence properties of the 2-block ADMM have been studied extensively in the literature. Specifically, it has been proven that the 2-blo…
The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the…
This work studies how an AI-controlled dog-fighting agent with tunable decision-making parameters can learn to optimize performance against an intelligent adversary, as measured by a stochastic objective function evaluated on simulated combat engagements. Gaussian process Bayesian optimization (GPBO) techniques are dev…
We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform. A series of computational experiments show that there exists an interesting similarity between the scatter plot of hidden parameters in a shallow ne…
Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.
problem Optimizing softmax policies with neural networks in the mean-field regime.
method Modeling neural networks as Wasserstein gradient flows and proving global optimality of fixed points.
result Global optimality of softmax policy gradient in wide single hidden layer neural networks with entropy regularization.
We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diver…
New NPG variants ensure parameter convergence in multi-agent learning.
problem Non-convergence of parameters in NPG for multi-agent learning.
method Proposed variants of NPG for multi-agent learning scenarios.
result Global last-iterate parameter convergence guarantees in various multi-agent learning settings.
This Ph.D. thesis is devoted to the constructions of Lagrangian formulation on Finsler and Kawaguchi manifolds. While Finsler geometry is a natural extension of Riemannian geometry, Kawaguchi geometry is the extension of Finsler geometry to higher order derivatives and to k-dimensional parameter space. The latter exten…