The study examines the supports of extremal martingale measures with given marginals in a two-period setting.
problem Investigating the supports of extremal martingale measures with pre-specified marginals in a two-period setting.
method Established equivalence between extremality and denseness in L1(Q), provided combinatorial sufficient conditions for weak exact predictable representation property (WEP), and studied the relation between cycles and extremality. result Developed necessary and sufficient conditions for the weak exact predictable representation property (WEP) in terms of 2-net and deadlock for finite support of the first marginal. The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.
problem Finding exact solutions to an Einstein-Dirac-Maxwell system with Sasakian quasi-Killing spinors.
method Constructing a family of exact solutions on four-dimensional static Sasakian spacetimes using the Sasakian frame.
result Closed and open universe models are found with specific energy conditions.
Fairness constraints improve exact recovery in structured prediction models.
problem Exact recovery of fair binary node labels from noisy observations.
method Analyzed Globerson et al. (2015) model with fairness constraints and improved exact recovery for graphs with poor expansion properties.
result Fairness constraints improve the probability of exact recovery from noisy observations.
Develops a diagrammatic method for symplectic filling classifications.
problem Classifying exact/weak symplectic fillings of 3D contact manifolds.
method Symplectic JSJ decomposition applied to contact surgery diagrams.
result Recover symplectic fillings for certain lens spaces and torus bundles, and classify fillings for a large class of plumbed 3-manifolds.
Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.
problem Understanding Anosov representations and their properties.
method Characterizations via equivariant limit maps, Cartan property, and uniform gap summation.
result Characterizations of Anosov representations and strongly convex cocompact subgroups.
Interpretable representations improve explainable AI by translating complex data into understandable concepts.
problem Many explainers use interpretable representations but overlook their full potential and assumptions.
method An in-depth analysis of interpretable representations for tabular, image, and text data, identifying strengths, weaknesses, and desiderata.
result Linear model quantifies interpretable concepts' influence on black-box predictions, revealing their explanatory properties and manipulability.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to Φ-weak convergence. result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.
New method for time series data ensures accurate predictions.
problem Time series data with potential serial dependence.
method Randomization method with block structures in permutation scheme.
result Retains exact validity for i.i.d. or exchangeable data.
Weak supervision challenges black-box models, suggesting fusion of modeling cultures.
problem Challenges of strong supervision in achieving accurate predictions.
method Integrating data modeling into algorithmic modeling for weak supervision.
result Integration of data modeling culture improves model stability and accuracy.
The paper provides a framework for weakly supervised disentanglement guarantees.
problem Learning disentangled representations in real-world data.
method Theoretical framework for analyzing disentanglement guarantees with weak supervision.
result Empirical verification of weak supervision methods' predictive power and usefulness.
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by t…
Paper defines weak representations and their equivalence to VB-groupoids.
problem Understanding representations of Lie groupoids and VB-groupoids.
method Introduces weak representations and shows equivalences between categories.
result Equivalence between 2-term representations up to homotopy and weak representations of G.
New method identifies stable latent variables across different domains using weak distributional invariances.
problem Learning causal representations for multi-domain datasets.
method Autoencoders incorporating weak distributional invariances.
result Autoencoders can identify stable latent variables across different domains.
Boosting framework for vector-valued prediction with geometric stability.
problem Lack of a general theoretical understanding of aggregation for structured prediction.
method Identifies (α,β)-stability property and proposes a boosting framework based on exponential reweighting and geometric-median aggregation. result Obtains exponential decay of empirical divergence error under weak learner condition and (α,β)-stability. ChemNet uses rule-based labels for weakly supervised learning to predict chemical properties.
problem Lack of labeled data in chemistry.
method Rule-based knowledge for training ChemNet, a deep neural network, on large unlabeled chemical databases.
result ChemNet outperforms DNN models trained with conventional supervised learning on smaller datasets.
New regularization method corrects over-shrinkage in small data regression.
problem Over-shrinkage in small data regression leading to underfitting.
method Negative-capable ridge family that permits negative regularization.
result Negative regularization acts as controlled anti-shrinkage, increasing effective complexity.
Study Anosov representations of reducible suspensions of hyperbolic groups.
problem Characterize dynamical properties of reducible suspensions of Anosov representations.
method Analyzing linear representations of non-elementary hyperbolic groups, focusing on weak unipotent actions on subspaces.
result Characterize when reducible suspensions are discrete and faithful, quasi-isometrically embedded, and Anosov.
ASTRA uses unlabeled data and weak rules to train deep models effectively.
problem Learning with weak supervision rules is challenging due to their heuristic and noisy nature.
method ASTRA framework that considers contextualized representations and pseudo-labels for unlabeled data, and a rule attention network to aggregate labels.
result Significant improvements over state-of-the-art baselines on text classification benchmarks.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
New varifold solutions for mean curvature flow converge and are unique.
problem Mean curvature flow and Allen-Cahn equation convergence and uniqueness.
method Evolving varifolds coupled to phase volumes, weak-strong uniqueness principle.
result Limits of Allen-Cahn solutions are varifold solutions, and classical flows are unique.
New theory explains how strong models can learn from weak ones.
problem Learning from weak, incomplete, or incorrect labels.
method New bounds based on data distribution and student hypothesis class.
result Existing weak supervision theory fails to account for pseudolabel correction and coverage expansion.
Weak labels can significantly speed up learning for strong tasks.
problem Learning with limited strong labels.
method Using weak labels to accelerate learning of strong tasks.
result Weak labels can accelerate learning to O(icefrac1n) rate. Paper verifies properties of binarized neural networks using SAT solvers.
problem Verifying properties of deep neural networks.
method Exact Boolean encoding of binarized neural networks, SAT solvers, counterexample-guided search.
result Demonstrates scalability to medium-size deep neural networks for robustness verification.
Simplicial spheres have a weak Lefschetz property in characteristic 2.
problem Proving the weak Lefschetz property for simplicial spheres.
method Using bistellar moves to show the property is preserved.
result The weak Lefschetz property is preserved by bistellar moves for PL-spheres.
Multimodal deep learning improves toxicity prediction accuracy.
problem Improving prediction accuracy of chemical compound toxicity.
method Combining multiple neural network types and data representations.
result Significantly better accuracy on a toxicity benchmark.
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous…
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
Study compares atom representations in graph neural networks for molecular properties.
problem Incorrect attribution of results in molecular property prediction due to varying atom features.
method Evaluated multiple atom representations on free energy, solubility, and metabolic stability predictions.
result Different atom representations can lead to varying predictive performance in graph neural networks.
New methods lift weak supervision to structured prediction, providing robustness guarantees.
problem Applying weak supervision techniques to structured prediction problems.
method Introducing pseudo-Euclidean embeddings, tensor decompositions, and invariants for consistent noise rate estimation.
result Generalization guarantees nearly identical to those for models trained on clean data.
We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the ex…
Deep neural nets learn from weakly dependent processes.
problem Learning from ψ-weakly dependent processes. method Deep neural networks for ψ-weakly dependent processes. result Established consistency of empirical risk minimization algorithm and generalization bound.
Paper tackles domain invariant sentiment classification using weak supervision.
problem Learning a sentiment classification model that adapts to any target domain.
method Two-stage training procedure with weakly supervised datasets.
result Transfer learning with weak supervision achieves performance close to supervised training.
MaxRR efficiently unlearns models by splitting and selecting core samples.
problem Efficiently unlearning models while verifying unlearning guarantees.
method Model splitting and core sample selection with a generalized unlearning metric.
result MaxRR achieves efficient unlearning with properties matching full retraining.
Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thurston's gluing equations that play an important role in recent developments of exact and perturbative Chern-Simons theory. In this paper, we …
Paper introduces methods for more reliable probabilistic predictions with confidence intervals.
problem Inaccurate labeling of datasets due to unreliable probabilistic predictions from weak labeling functions.
method Proposes a methodology to provide confidence intervals for label probabilities using uncertainty sets of distributions.
result Improves reliability of probabilistic predictions and provides confidence intervals for label probabilities.
WeLa-VAE learns interpretable disentangled representations with weak supervision.
problem Learning disentangled representations without strong supervision.
method Variational inference framework with shared latent variables and modified variational lower bound.
result WeLa-VAE learns alternative disentangled representations (polar) from weak labels (distance and angle) without refined supervision.
Flexible framework for modeling predictive distributions of time series
problem Modeling predictive distributions of nonlinear time series
method Generative adversarial networks
result Direct simulation-based approximation to predictive distributions
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult …
RECS improves graph embeddings by preserving network structure and stability.
problem Stable and accurate graph embeddings for multi-graph problems.
method RECS uses connection subgraphs and analogy to graphs with electrical circuits to learn stable node representations.
result RECS outperforms state-of-the-art algorithms by up to 36.85% on multi-label classification problems.
Subset selection improves weak supervision performance.
problem Optimizing the use of weakly-labeled data.
method Combining pretrained data representations with the cut statistic for subset selection.
result Subset selection improves weak supervision performance by up to 19%.
Self-affine arcs without inner weak separation are parabolic segments.
problem Characterizing self-affine Jordan arcs without parabolic segments.
method Analyzing the weak separation property and proving implications for arc types.
result Self-affine Jordan arcs without parabolic segments are attractors of multizippers.
Formulates Markov property for risk-sensitive dynamic optimisation.
problem Risk-sensitive dynamic optimisation problems in discrete time.
method Formulates probabilistic Markov property under dynamic risk framework.
result Property holds for standard risk measures and has multiple equivalent versions.
New approach identifies latent properties from mechanisms, not just data.
problem Identifying latent properties from data generating processes.
method Equivariance perspective on identifiable representation learning.
result Identification of latent properties is possible up to shared equivariances in known mechanisms.
Study evaluates margin parameter effects on knowledge embedding quality.
problem Understanding margin parameter's impact on embedding quality.
method Examined margin parameter values for multi-relational categorized data.
result Lower margin values are insufficient, while larger values cause noise.
Algorithm selects best sensor tests for unknown outcomes.
problem Selecting optimal sensors in unsupervised systems.
method Developed an algorithm for stochastic partial monitoring under Weak Dominance property.
result Algorithm achieves sub-linear regret in sensor selection.
Paper finds exact global optima for adversarial representation learning.
problem Obtaining data representations invariant to sensitive attributes.
method Spectral learning for linear functions, kernel representation for non-linear functions.
result Exact closed-form expression for global optima with performance guarantees.
A new framework using kernel packets overcomes limitations of state space models for multi-dimensional data.
problem Computational limitations of Gaussian process regression in large-scale applications.
method Kernel packet approach, identifying KPs via forward and backward state space representations.
result Exact, memory-efficient inference with linear-time training and logarithmic/predictive time.