Study LASSO for high-dimensional VAR models with weakly dependent innovations.
problem Understanding sparse regularization in high-dimensional VAR models with weakly dependent innovations.
method LASSO estimation for weakly sparse VAR models with heavy tailed innovations, under L1 mixingale condition. result Oracle properties of LASSO estimation in high-dimensional VAR models with weakly dependent innovations.
The paper improves generalization bounds for classifier chains with interdependent labels.
problem Improving generalization for classifier chains with multiple interdependent labels.
method Using large deviation inequalities for weakly dependent sequences, the paper derives a new generalization error bound.
result The derived bound explicitly shows dependencies between class labels and provides insights into the chain's order.
Improved GEC with weakly supervised data and iterative decoding.
problem Grammatical error correction using limited labeled data.
method Transformer model trained on weakly supervised bitext, iterative decoding.
result Iterative decoding improves GEC performance on CoNLL'14 benchmark.
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
QLSTM improves speech recognition by considering internal quaternion dependencies.
problem Weak internal dependencies in traditional RNNs for speech recognition.
method Proposes QLSTM, a quaternion-based LSTM that considers both external and internal dependencies.
result QLSTM achieves better performance with up to 2.8 times fewer parameters.
Novel ramp loss method improves weakly supervised machine translation and parsing.
problem Training neural models without gold labels in weak supervision scenarios.
method Adapted ramp loss objectives to promote positive outputs and discourage negative ones.
result Bipolar ramp loss objectives outperform other methods on weakly supervised tasks.
Paper presents a neural network for recognizing human activities from unlabeled sensor data.
problem Time-consuming annotation of sensor data for activity recognition.
method Attention-based convolutional neural network for weakly labeled data.
result Attention model improves accuracy in recognizing human activities.
We show that for any weakly convergent sequence of ergodic SL2(R)-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel-Veech constants converge to the Siegel-Veech constant of the limit measure. Together with a measure equidistribution result due to Eskin-M…
The paper develops a deep neural network estimator for weakly dependent processes with various loss functions.
problem Learning weakly dependent processes with a broad class of loss functions.
method Sparse-penalized deep neural networks with ψ-weak dependence structure and θ∞-coefficients. result Oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators.
New method improves tensor completion for weakly-dependent spatiotemporal data.
problem Improving tensor completion for weakly-dependent data on graphs.
method Introducing L1-norm and Graph Laplacian penalties for low-rank tensor decomposition and completion. result Improved performance in metro passenger flow prediction.
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.
We give the definition of angles on a Gromov-Hausdorff limit space of a sequence of complete n-dimensional Riemannian manifolds with a lower Ricci curvature bound. We apply this to prove there is a weakly second order differential structure on these spaces and prove there is a unique Levi-Civita connection allowing us …
Paper develops algorithms for solving non-convex non-concave problems with applications in GAN training.
problem Solving non-convex non-concave min-max saddle-point problems.
method Inexact proximal point method with strongly monotone mappings.
result First-order convergence to a nearly stationary solution of the original min-max problem.
The paper bounds the excess risk of deep neural networks for weakly dependent processes.
problem Learning with weakly dependent data using deep neural networks.
method Approximation of smooth functions by deep neural networks and a bound on excess risk.
result The excess risk bound for deep learning under weak dependence is close to O(n−1/2) for sufficiently smooth functions. We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filtered and filtered diffeological spaces, whose tangent spaces are easier to understand. These are the diffeological spaces whose categories o…
Algorithm transforms weakly negative plumbing trees to negative definite ones.
problem Transforming weakly negative plumbing trees to negative definite ones.
method Combining plumbing calculus with diagonalization algorithm to systematically eliminate positive eigenvalues.
result Explicit algorithm reduces weakly negative definite plumbing trees to negative definite ones.
Study Betti numbers of manifolds converging to covers, deriving new convergence results.
problem Analyzing Betti numbers of manifolds converging to their covers.
method Benjamini-Schramm convergence, Price inequalities, refined Thick-Thin decomposition, Moser iteration.
result Convergence results for weakly uniform discrete sequences of closed Riemannian manifolds under negative Ricci curvature.
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which cover all elliptic, overdetermined elliptic, subelliptic and parabolic…
Characterizes stable minimal capillary surfaces with specific angles.
problem Understanding stable minimal capillary surfaces with near 0 or π angles. method Curvature estimates for sequences of weakly stable minimal capillary surfaces.
result Characterization of tangential limits of stable minimal capillary surfaces.
Develops a hybrid model for text summarization.
problem Summarizing long text sequences concisely.
method Extends sequence encoders with a graph component to handle long-distance relationships in text.
result Hybrid models outperform pure sequence or graph models on summarization tasks.
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.
problem Tackles robust deep learning from weakly dependent data with unbounded loss and input.
method Establishes non-asymptotic bounds for expected excess risk under strong mixing and ψ-weak dependence assumptions. result Derives a relationship between bounds and r, and shows convergence rate close to i.i.d. results for r=∞. The paper proves stability of critical points for conformally invariant Lagrangians.
problem Stability of critical points for conformally invariant Lagrangians under weak convergence.
method Upper-semi-continuity of Morse index plus nullity established for critical points.
result The sum of Morse indices and nullity is bounded from above by the sum of the Morse indices plus the nullity of the weak limit and bubbles.
The study finds knots with specific surgeries that don't allow weak symplectic fillings.
problem Detecting weakly symplectic fillability of L-space knots after positive surgeries. method Analyzing arithmetic data from knot type and surgery coefficients to compute geometric invariants.
result Provides an infinite family of hyperbolic L-spaces that do not admit weakly symplectic fillings. Study continuity of limit sets in symmetric spaces.
problem Continuity of limit sets for geometrically finite subgroups in symmetric spaces.
method Extended geometrically finite representations theory.
result Limit sets vary continuously with respect to Hausdorff distance under strong convergence.
Paper describes links of mixed polynomials with specific properties.
problem Understanding the links of mixed polynomials with nice Newton boundaries.
method Analyzes links constructed from sequences of links associated with compact 1-faces of the Newton boundary.
result Links of singularities of inner non-degenerate mixed polynomials can be described using a specific procedure.
As machine learning algorithms become increasingly sophisticated to exploit subtle features of the data, they often become more dependent on simulations. This paper presents a new approach called weakly supervised classification in which class proportions are the only input into the machine learning algorithm. Using on…
Flat Yang-Mills connections on pinched manifolds.
problem Stability of Yang-Mills connections on compact manifolds.
method Pinching conditions and weak stability criteria.
result No non-flat weakly stable Yang-Mills connections on δ(n)-pinched compact simply-connected Riemannian manifolds.
Study differentially private methods for learning Hawkes processes.
problem Lack of thorough analysis on sample complexity for learning Hawkes processes parameters and releasing differentially private versions.
method Developed non-private and differentially private estimators for Hawkes processes parameters.
result Obtained sample complexity results for both private and non-private settings.
Study shows convergence of Fubini-Study currents to equilibrium metrics on Kähler manifolds.
problem Convergence of Fubini-Study currents to equilibrium metrics in Kähler geometry.
method Analysis of continuous Hermitian metrics and their Fubini-Study currents on line bundles.
result The scaled difference between Fubini-Study currents and equilibrium metrics converges to zero in the sense of currents.
Paper proposes an algorithm for sampling from complex mixture distributions without requiring smoothness.
problem Sampling from a mixture of weakly smooth potentials.
method Unadjusted Langevin algorithm with Euler discretization for a mixture of weakly smooth distributions.
result Convergence in Kullback-Leibler divergence and Lβ-Wasserstein metric with polynomial dependence on dimension. MixML unifies analysis of weakly consistent parallel learning.
problem Lack of insight into how communication structure affects convergence in parallel learning.
method Proposes MixML framework for analyzing convergence of weakly consistent parallel machine learning.
result Shows dependency of convergence on mixing time tmix.
We consdier in dimension four weakly convergent sequences of approximate biharmonic maos into sphere with bi-tension fields bounded in Lp for some p>1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on $\mathbb…
RAN model recognizes multiple activities from unlabeled sensor data.
problem Handling weakly labeled multi-activity data from wearable sensors.
method Recurrent Attention Networks (RAN) for sequential multi-activity recognition and localization.
result RAN model can infer multiple activities and determine activity locations from unlabeled data.
Efficiently predicts paths in hierarchical text classification using unlabeled data.
problem Costly labeling of documents in hierarchical text classification.
method Path cost-sensitive learning algorithm using generative model and path constraints.
result Significantly reduces computational cost and improves efficiency.
Method approximates Lipschitz domains with smoother shapes.
problem Approximating bounded Lipschitz domains.
method Sequence of smooth, bounded domains with weak curvatures.
result Uniform isocapacitary estimates for approximating sets.
The paper examines compactness of scalar curvature sequences on conformal manifolds.
problem Compactness of sequences of Riemannian manifolds with positive scalar curvature.
method Analyzes the conformal case of Riemannian manifolds, focusing on compactness and convergence properties.
result Compactness of conformal factors and C0 convergence away from a singular set. Paper analyzes convergence of stochastic methods under heavy-tailed noise.
problem Analyzing convergence of stochastic methods under heavy-tailed noise.
method Investigates vanilla and clipped stochastic subgradient descent methods.
result Demonstrates convergence properties under sub-Weibull and p-BCM noise assumptions.
Study on harmonic maps from surfaces to homogeneous spaces, focusing on bubble formation and geometric constraints.
problem Understanding the behavior of harmonic maps from surfaces to homogeneous spaces, especially in the presence of bubbles.
method Refined asymptotic expansions and obstruction relations for sequences developing a single bubble, geometric constraints for weakly conformal maps.
result New geometric constraints on the tangent planes of the limit map and bubble, depending on the dimensionality.
Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.
problem Understand the global structure of spacetimes with weakly trapped surfaces.
method Show foliation of MOTS generating totally geodesic null hypersurfaces.
result Obtain local or global rigidity results based on assumptions.
Study Kähler metrics on complex tori with almost non-negative scalar curvature.
problem Stability of Kähler metrics on complex tori.
method Proved convergence of non-collapsing subsequence of Kähler metrics to flat torus.
result Kähler metrics with almost non-negative scalar curvature on complex tori converge to flat torus.
We consider the task of training classifiers without labels. We propose a weakly supervised method---adversarial label learning---that trains classifiers to perform well against an adversary that chooses labels for training data. The weak supervision constrains what labels the adversary can choose. The method therefore…
Optimizes learning policies in MDPs with weakly communicating structure.
problem Learning optimal policies in weakly communicating MDPs with generative model.
method Span-based approach, reducing to discounted MDPs for analysis.
result First minimax optimal sample complexity bound for weakly communicating MDPs.
Differentiable losses for combinatorial optimization problems in sequence modeling.
problem Mismatch between training and inference objectives in sequence models.
method Gradient descent over linear programs representing combinatorial optimization problems.
result Gradient descent can be applied to combinatorial optimization problems efficiently.
Many advanced Learning from Demonstration (LfD) methods consider the decomposition of complex, real-world tasks into simpler sub-tasks. By reusing the corresponding sub-policies within and between tasks, they provide training data for each policy from different high-level tasks and compose them to perform novel ones. E…
We organize the quantum hyperbolic invariants (QHI) of 3-manifolds into sequences of rational functions indexed by the odd integers N≥3 and defined on moduli spaces of geometric structures refining the character varieties. In the case of one-cusped hyperbolic 3-manifolds M we generalize the QHI and get rati…
Unified approach for multicalibration in weakly supervised learning.
problem Existing multicalibration methods require clean input-label pairs, which are unavailable in weakly supervised learning.
method Developed estimators and post-hoc correction methods for multicalibration under weak supervision.
result Unified framework for estimating and correcting multicalibration under weak supervision with finite-sample guarantees.
We prove that a sequence of possibly branched, weak immersions of the two-sphere S2 into an arbitrary compact riemannian manifold (Mm,h) with uniformly bounded area and uniformly bounded L2−norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a sub…