Corrects an earlier theorem, establishing new facts about information structures and non-anticipative aggregation.
problem The nature of information structures and their impact on non-anticipative aggregation.
method Local reduction of pricing to the natural price filtration, stability properties, and the establishment of new facts.
result Non-anticipative signals can reveal future information, requiring dependence among signals (masking relation) and not independence.
Derives functional Itô formula for non-anticipative maps of rough paths.
problem Functional Itô formula for non-anticipative maps of càdlàg rough paths.
method Approximation properties of the signature and Marcus transformation.
result Functional Taylor expansion for sufficiently regular non-anticipative maps.
MELO predicts electricity loads by adapting to shifts without external indicators.
problem Adapting to non-stationary prediction challenges in online settings.
method MELO combines multiple forgetting factors and aggregation rules to adaptively predict.
result MELO reduces RMSE by 34.7% compared to base predictors and external covariates.
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Alòs in [2] for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used are non anticipative. …
Model predicts stationary equilibrium in investment decisions of firms in fluctuating markets.
problem Investment decisions in fluctuating markets with varying volatility and commodity prices.
method Mean-field model with Gaussian productivity shocks and two-state Markov chain for macroeconomic events.
result Existence, uniqueness, and characterization of stationary mean-field equilibrium with barrier-type investment strategy.
Universal approximation for stochastic processes using Brownian motion.
problem Approximating stochastic processes with linear functionals.
method Establishing Lp-type universal approximation theorems for rough path spaces. result Linear functionals on the signature of time-extended Brownian motion can approximate any p-integrable stochastic process. We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of Itô's integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlle…
Universal approximation theorem for differentiable maps on infinite-dimensional manifolds
problem Approximation of differentiable maps on infinite-dimensional manifolds
method Weighted universal approximation theorem
result Universal approximation theorem for differentiable maps
On a filtered probability space (Ω,F,P,F=(Ft)t=0,…,T), we consider stopper-stopper games $\overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{τ\in\T}\E[U(\Rho(τ),τ)]$ and $\underline V:=\sup_{\Tau\in\bT^i}\inf_{ρ\in\T}\E[U(\Rho(τ),τ)]$ in discrete time, where U(s,t) is $\mathcal{F}_{s\vee…
We develop a Markovian approximation for SVV models to compute hedging strategies.
problem Computing optimal hedging strategies for SVV models with non-Markovian noise.
method Develop a Markovian approximation of the Volterra noise kernel to compute hedging strategies.
result Error estimates for the approximation of volatility, prices, and optimal hedge.
Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.
problem Approximating differentiable maps on infinite-dimensional manifolds.
method Proves a weighted Nachbin theorem to establish universal approximation for differentiable maps, including derivatives.
result Linear functions of the signature can approximate path space functionals including their derivatives.
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…
Proposes a new optimization-based method for aggregating sets in neural networks.
problem Limited representational power of existing aggregation methods.
method Equilibrium Aggregation: an optimization-based approach.
result Equilibrium Aggregation outperforms existing methods in various tasks.
Functional input neural networks approximate continuous functions on weighted spaces.
problem Approximating continuous functions on infinite-dimensional weighted spaces.
method Additive family mapping, non-linear activation, linear readouts, Stone-Weierstrass theorem.
result Global universal approximation of continuous functions on weighted spaces.
Study aggregation of statistical evidence under unknown dependence using group-invariance.
problem Aggregating statistical evidence under unknown and complex dependence structures.
method Develops a framework using group-invariance and permutation-based constructions to aggregate evidence across transformed datasets.
result Shows uniform improvement in critical values for single-batch aggregation over deterministic calibrations, adapting to unknown dependence structures.
New LCM aggregator improves GNN performance and efficiency.
problem Graph neural networks' sensitivity to aggregation function choice.
method Learnable commutative monoid for graph aggregation.
result LCM aggregator achieves performance competitive with recurrent aggregators.
Unified approach to aggregating models and preferences.
problem Consistent aggregation of models and preferences.
method Formal definition and weighted averaging of models and preferences.
result All rational aggregation rules are weighted averages of highest-ranked models/experts.
Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In par…
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregatio…
Aggregation challenges causal interpretation of IV estimators.
problem Aggregation of fine-grained components into an aggregate treatment variable.
method Characterization of conditions for identifying aggregate causal effects.
result Standard IV estimators cannot identify aggregate causal effects due to ambiguous dependencies.
SACP aggregates nonconformity scores from multiple predictors to create more efficient uncertainty sets.
problem Combining predictive uncertainties from multiple models for efficient and reliable uncertainty quantification.
method SACP (Symmetric Aggregated Conformal Prediction) aggregates nonconformity scores using a flexible symmetric aggregation function.
result SACP consistently improves efficiency and often outperforms state-of-the-art model aggregation baselines.
We consider the forecast aggregation problem in repeated settings, where the forecasts are done on a binary event. At each period multiple experts provide forecasts about an event. The goal of the aggregator is to aggregate those forecasts into a subjective accurate forecast. We assume that experts are Bayesian; namely…
We introduce a novel aggregation method to efficiently perform image denoising. Preliminary filters are aggregated in a non-linear fashion, using a new metric of pixel proximity based on how the pool of filters reaches a consensus. We provide a theoretical bound to support our aggregation scheme, its numerical performa…
Paper analyzes sparse aggregation in GLMs with Kullback-Leibler risk bounds.
problem Sparse aggregation in GLMs for parameter approximation.
method Exponential weighted aggregation scheme with Kullback-Leibler risk bounds.
result Sharp oracle inequality for Kullback-Leibler risk with leading constant 1 and minimax-optimal rate of aggregation.
Aggregates predictions from multiple regression models using random projections and kernel methods.
problem Combining predictions from multiple regression models to improve accuracy.
method Random projection of high-dimensional feature space, followed by kernel-based consensual aggregation.
result The aggregation scheme performs similarly to using the original high-dimensional features, with high probability.
The paper introduces a method to control false splits in tree-based data aggregation.
problem Identifying the correct subgroups to treat as a single entity in tree-based data.
method Introduces the 'false split rate' and proposes a multiple hypothesis testing algorithm for tree-based aggregation.
result The proposed algorithm controls the false split rate, demonstrating its effectiveness on stock volatility and taxi fare data.
We show LLMs can be locally linear, enabling better control of activations.
problem Suboptimal control of LLM activations during generation.
method Model LLM inference as a linear dynamical system, compute feedback controllers using Jacobians, and adapt classical control theory.
result Robust, fine-grained control of LLM activations across models and tasks.
Estimates variance function using aggregation methods in regression models.
problem Estimating variance function in regression models.
method Two-step procedure involving model selection or convex aggregation, using two independent samples.
result Consistency of the proposed method in L2 error for MS and C aggregations.
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
Paper presents a novel approach for global feature aggregation in Graph Neural Networks.
problem Graphs lack a straightforward way to perform non-local feature aggregation like images and texts.
method Utilizes Latent Fixed Data Structure (LFDS) to aggregate feature vectors from local extraction.
result Proposed methods achieve competitive or better results with linear computational complexity.
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
New method aggregates nodes in sparse graphical models.
problem Estimating edge-sparse graphical models.
method Tree-aggregated graphical lasso (tag-lasso) method.
result Aggregates nodes in a data-driven fashion using a tree.
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: ag…
U-aggregation combines multiple models without labels for better risk prediction.
problem Challenges in selecting best model for new populations due to limited data and lack of true labels.
method U-aggregation, an unsupervised model aggregation method that integrates pre-trained models without observed labels.
result U-aggregation improves genetic risk prediction of complex traits using publicly available models.
BOA improves financial forecasting by combining expert models.
problem Challenges in choosing between multiple machine learning models for financial forecasting.
method Online aggregation of expert models using Bernstein Online Aggregation (BOA) procedure.
result BOA leads to better portfolio performance, higher Sharpe Ratio, and lower shortfall.
MEVA aggregates model predictions to improve accuracy without needing model details.
problem Improving model accuracy by combining multiple models.
method Non-intrusive, data-driven framework that treats models as black boxes and optimizes aggregation methods.
result MVA outperforms MEA in estimating aggregated predictions, enhancing robustness and accuracy.
New aggregation method improves GNN robustness to structural perturbations.
problem Graph Neural Networks (GNNs) are vulnerable to adversarial attacks that manipulate graph structure.
method Proposes a robust aggregation function with a breakdown point of 0.5, inspired by robust statistics.
result Improves GNN robustness by a factor of 3 on Cora ML and 5.5 on Citeseer, and 8 for low-degree nodes.
A new algorithm estimates aggregate marginals from noisy data in an online manner.
problem Estimating aggregate marginals of a Markov chain from noisy aggregate observations.
method Sliding window Sinkhorn belief propagation (SW-SBP) algorithm.
result Demonstrated improved performance on inferring population flow.
Non-affine aggregation rules cannot preserve monotonicity in convex learning.
problem Designing non-affine aggregation rules that maintain monotonicity in convex learning.
method Proving that monotonicity of aggregated gradients is preserved only if the aggregation rule is positively affine.
result Non-affine aggregation prevents steady convergence and substantially degrades algorithmic stability.
Study improves fair opinion aggregation by balancing voter attributes.
problem Aggregation of opinions can be biased by voter attributes.
method Combines majority voting and D&S model with fairness options.
result Effective combination of Soft D&S and fairness options for different data types.
Fishnets improve set and graph learning with scalable, robust aggregation.
problem Learning informative embeddings for sets and graphs with scalable and robust aggregation.
method Proposes Fishnets, a new aggregation strategy for set-based learning.
result Fishnets achieve state-of-the-art performance on graph datasets with fewer parameters and faster training.
CAggNet improves medical image segmentation by fusing coarse and fine features.
problem Medical image segmentation accuracy and efficiency.
method Crossing Aggregation Network with nested skip connections and weighted aggregation.
result CAggNet achieves more accurate and efficient segmentation compared to existing methods.
Study improves forecasting of aggregated curves in electricity markets.
problem Improving accuracy in predicting aggregated curves like demand and supply in electricity markets.
method Exploits hierarchical structure of aggregated curves, uses reconciliation methods (bottom-up, top-down, linear optimal, aggregated-down).
result Hierarchical reconciliation methods can significantly improve forecast accuracy of aggregated curves.
Productivity and credit limits affect aggregate production in non-monotonic ways.
problem Understanding how aggregate production is influenced by individual characteristics and financial constraints.
method Analytical proof of non-monotonic effects of productivity and credit limits on aggregate production in a general equilibrium model.
result Equilibrium aggregate production can be non-monotonic in both individual productivity and credit limit.
The paper proposes criteria and methods for evaluating and aggregating feature-based model explanations.
problem Lack of quantitative evaluation criteria for feature-based model explanations.
method Developed quantitative evaluation criteria (low sensitivity, high faithfulness, low complexity), devised a framework for aggregation, and derived a new aggregate Shapley value explanation function.
result A new aggregate Shapley value explanation function that minimizes sensitivity.
Multidimensional data have become ubiquitous and are frequently encountered in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location. We often have access to multiple aggregated views of the same data, each aggregated i…
Optimal fuzzy classification aggregation functions are weighted means.
problem Characterizing optimal fuzzy classification aggregation functions.
method Proving optimality of weighted arithmetic means for fuzzy classification.
result Optimal fuzzy classification aggregation functions are weighted means.
Study risk aggregation with order constraint under unknown dependence.
problem Risk aggregation with an order constraint under uncertainty.
method Introduced DL coupling for concave order risk aggregation, generalized to tail risk measures.
result Analytical formulas for bounds on Value-at-Risk with improved accuracy.