We discuss the general properties of the theory of joint invariants of a smooth Lie group action in a manifold. Many of the known results about differential invariants, including Lie's finiteness theorem, have simpler versions in the context of joint invariants. We explore the relation between joint and differential in…
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48 results for “joint smoothness”
Estimates multiple linear systems on a graph with smoothness constraints.
problem Joint estimation of multiple linear systems under graph smoothness constraints.
method Proposes estimators for joint estimation of system matrices with error bounds.
result MSE converges to zero as increases, typically polynomially fast w.r.t .
This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth vector field. The result is stated in Theorem 1.4.
Efficiently estimates online variational learning using importance sampling.
problem Online variational estimation in state-space models.
method Variational approach with Monte Carlo importance sampling.
result Proposed efficient algorithm for streaming data.
We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and …
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting…
Optimal online learning for joint pricing and resource allocation.
problem Maximizing net profit in dynamic pricing and resource allocation with stochastic demand.
method Developed an efficient algorithm using a Lower-Confidence Bound (LCB) meta-strategy over multiple OCO agents.
result Achieved regret, optimal with respect to time horizon .
The problem of joint feature selection across a group of related tasks has applications in many areas including biomedical informatics and computer vision. We consider the l2,1-norm regularized regression model for joint feature selection from multiple tasks, which can be derived in the probabilistic framework by assum…
We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed two families of plane curves with second order contact at the envelope.
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure …
New smooth models for string groups defined in ∞-categories.
problem Defining string group models in smooth spaces.
method Homotopy-theoretic definition using singular complex functor.
result New smooth models for the string group.
New method for LVEBMs using saddle-point optimization and Langevin updates.
problem Expressive generative modeling of latent variables with hidden structure.
method Reformulate LVEBM training as a saddle problem, using Langevin updates and gradient flows.
result Proves existence and convergence of the algorithm under standard assumptions, with improved ELBO bounds.
A conjecture of Kotschick predicts that a compact Kähler manifold fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao, we use our approach to prove Kotschick's…
While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement f…
This expository paper, based on a Current Events Bulletin talk at the January, 2016 Joint Meetings, introduces the concept of Lyapunov exponents and discusses the role they play in three areas: smooth ergodic theory, Teichmüller theory, and the spectral theory of one-frequency Schrödinger operators. The inspiration for…
A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Modelsstat.ML
Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large ) under a high-dimensional (large ) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult n…
A new method for joint noise removal and trend estimation from sparse signals.
problem Jointly removing noise and estimating trends from sparse signals.
method PENDANTSS combines SOOT/SPOQ penalties with BEADS algorithm in a Trust-Region block alternating variable metric forward-backward approach.
result Outperforms comparable methods in deconvolving analytical chemistry signals.
Proposes a spectral method for jointly smooth functions on multiple manifolds.
problem Registering measurements from different sensors and rejecting noise.
method Two steps: kernel subspace span and spectral method.
result Guaranteed orthogonal functions that are as jointly smooth as possible.
The paper proves regularity of states on manifolds with unstable dynamics.
problem Propagation of regularity in dynamical systems with unstable manifolds.
method Leafwise semiclassical pseudodifferential calculus adapted to foliated spaces.
result Pollicott-Ruelle resonant states are smooth over entire manifolds if smooth on unstable leaves.
We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization mode…
We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions.…
NeuralFLoC unifies registration and clustering of functional data, overcoming phase variation challenges.
problem Challenges in clustering functional data due to phase variation and temporal misalignment.
method NeuralFLoC uses Neural ODE-driven diffeomorphic flows and spectral clustering for joint registration and clustering.
result NeuralFLoC effectively disentangles phase and amplitude variation, achieving state-of-the-art performance.
A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.
problem Noise-robustness vs. data-consistency in Cryo-EM 3D map reconstruction.
method Ellipsoidal support lifting (ESL) for regularizing and approximating the global minimizer over Riemannian manifolds.
result The induced bias due to regularizing effect of ESL estimates better rotations than global optimisation.
We consider branes $N=I\times\so$, where $\so$ is an \ndash dimensional space form, not necessarily compact, in a Schwarzschild-AdS_{(n+2)} bulk $\mc N$. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the sin…
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
Survey on 4-manifolds with specific curvature properties.
problem Understanding the structure of 4-manifolds with nonnegative Ricci curvature and Euclidean volume growth.
method Analysis of blow-downs and cone-like structures at infinity.
result Manifolds look like cones over spherical space forms at infinity.
Estimates smooth graph signals from partial measurements.
problem Estimating latent signals on a graph from limited measurements.
method Smoothness penalized least squares estimator.
result Weak consistency for joint recovery of signals under stringent sampling.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
Paper constructs moduli spaces of Higgs bundles and connects them to Teichmüller space structures.
problem Constructing moduli spaces of Higgs bundles on varying Riemann surfaces.
method Gauge theoretic construction, Teichmüller space, isomonodromic foliation, Atiyah-Bott-Goldman symplectic structure.
result Surprising relationships between Higgs bundles, isomonodromic foliation, and Teichmüller space structures.
Improved state estimation in nonlinear models using amortized backward variational inference.
problem State estimation in general state-space models.
method Amortized backward variational inference with neural network parameters.
result Linear growth of variational approximation error in number of observations.
FJS method improves multinomial classification accuracy.
problem Improving multinomial classification accuracy under dataset shift.
method Derive FJS representation and propose alternative methods.
result Factorizable joint shift is not fully identifiable without additional assumptions.
On evaluation of joint risk for non-negative multivariate risks under dependence uncertaintyq-fin.RM
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
Introduces joint Shapley values to measure feature importance in models.
problem Measuring the importance of feature sets in machine learning models.
method Extends Shapley's axioms to measure a set of features' average contribution to a model's prediction.
result Joint Shapley values provide unique insights and are more consistent with local intuitions.
Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMmath.OC
The paper analyzes mirror descent in measure spaces and its applications.
problem Optimizing convex functionals over measure spaces.
method Derives convergence of mirror descent for relatively smooth and convex pairs of functionals.
result Shows Sinkhorn's primal iterations and EM as mirror descent.
Degenerations of rank-two bundles on threefolds lead to isolated point singularities, with rigidity and bubbling properties.
problem Degenerations of rank-two vector bundles on complex threefolds to a rank-two torsion-free sheaf with an isolated point singularity.
method Proving a rigidity identity and using it to obtain smoothability obstructions and construct local smoothings.
result Smoothability obstructions and local smoothings are obtained, with a rigidity identity linking algebraic bubbling multiplicity and Ext-length.
Study proposes a new model for joint survival annuity valuation.
problem Valuation of joint survival annuities and options.
method Linear-rational Wishart mortality model based on stochastic matrix affine process.
result Derives closed-form expression for joint survival annuity and option.
Estimates joint causal effects using single-variable interventions on nonlinear models.
problem Estimating joint causal effects from single-variable interventions.
method Identifiability result and practical estimator for decomposing causal effects.
result Joint effects can be inferred without joint interventional data for nonlinear additive models.
Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimizationcs.LG
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables an…
Study joint invariants on symplectic spaces, extending group and space variations.
problem Computing joint invariants on linear symplectic spaces.
method Review and extend previous work on group and space variations, relate to differential invariants.
result New computations and extensions of joint invariants.
Joint, Partially-joint, and Individual Independent Component Analysis in Multi-Subject fMRI Datastat.ML
Objective: Joint analysis of multi-subject brain imaging datasets has wide applications in biomedical engineering. In these datasets, some sources belong to all subjects (joint), a subset of subjects (partially-joint), or a single subject (individual). In this paper, this source model is referred to as joint/partially-…
Study immersions of surfaces into SL(2,C) and geodesics space.
problem Classical theory of hypersurfaces in pseudo-Riemannian space forms.
method Holomorphic Riemannian space forms and geodesics space of hyperbolic space.
result Characterization and construction of immersions.
Proposes joint LCA for multiview data to identify shared and view-specific components.
problem Extracting shared components sequentially from multiview data.
method Formulates a matrix decomposition model with joint and individual structures, proposes a penalty term objective function, and employs a refitting procedure.
result Achieves simultaneous estimation and rank selection for cross covariance.
AJL framework detects dynamic patterns in high-dimensional time-varying models.
problem Complex time-varying associations and abrupt regime shifts in longitudinal processes.
method Hierarchical regularization framework integrating functional variable selection with structural changepoint detection.
result The refined estimator achieves the oracle property in ultra-high-dimensional settings.
Joint diffusion models improve data representation for both generation and prediction.
problem Inconsistent performance between generation and classification tasks in joint models.
method Extended vanilla diffusion model with a classifier for joint end-to-end training.
result Joint diffusion model outperforms state-of-the-art hybrid methods in classification and generation.
Dynamic angles estimated from noisy measurements over time with smoothness constraints.
problem Recovering angles from noisy pairwise measurements over time.
method Three algorithms for joint estimation of angles under smoothness constraints.
result MSE converges to zero as increases under milder conditions.
Paper tackles dynamic behavior of variable topology mechanisms, presenting new transition conditions.
problem Dynamic behavior of mechanisms with changing kinematic topology.
method Presented new transition conditions for variable topology mechanisms using projected motion equations and Voronets equations.
result Results show the dynamic behavior of joint locking in 3R and 6DOF mechanisms.
The Neural Testbed evaluates joint predictions of neural agents, revealing their limitations.
problem Evaluating the quality of joint predictions generated by neural agents.
method Developed an open-source benchmark (The Neural Testbed) to assess agents' marginal and joint predictions.
result Popular Bayesian deep learning agents perform poorly on joint predictions, even with accurate marginal predictions.
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…