This work introduces a method to learn dynamical systems from noisy sensor measurements using multiple shooting.
problem Learning dynamical systems from noisy sensor measurements is challenging due to system instability.
method A scalable method based on multiple shooting.
result Robust learning of latent representations of dynamical systems from noisy measurements.
The paper proposes a new system ID method from noisy data.
problem System identification of linear and nonlinear non-autonomous systems from noisy and sparse data.
method Bayesian formulation for learning a hidden Markov model with stochastic dynamics, analyzed in the context of least squares and multiple shooting approaches.
result The proposed approach outperforms existing methods in terms of mean squared error and model generalizability.
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
problem Efficiently solving initial value problems for ODEs and PDEs.
method Leveraging time-parallel methods, MSLs use parallelizable root-finding algorithms.
result MSLs offer significant speedups in NFEs and inference time.
In this work we study the geodesic structure of the space Σ(X) of compact balls of a complete and locally compact metric length space endowed with the Hausdorff distance dH. In particular, we focus on a geometric condition (referred to as the shooting property) that enables us to give an explicit isometry between …
The paper finds curves minimizing elastic energy pinned at endpoints.
problem Finding curves that minimize elastic energy with fixed endpoints.
method Applying the shooting method to identify and classify critical points.
result Critical points consist of wavelike elasticae, and minimizers have no loops or interior inflection points.
Randomized gradient-based ensemble improves prediction accuracy.
problem Improving prediction accuracy in machine learning.
method Randomization and gradient-based aggregation of weakly-correlated estimators.
result The method outperforms existing techniques in terms of increased accuracy.
Bayesian Neural ODEs improve vessel trajectory prediction with better uncertainty estimates.
problem Challenges in predicting vessel trajectories from irregular AIS data.
method Adopted a Gaussian process (GP) kernel-based prior on the vector field evaluated at measurement points, combined with probabilistic multiple shooting for long trajectories.
result Improved accuracy and uncertainty quantification in vessel trajectory predictions.
Modified curve shortening flow constructs λ-Angenent curve.
problem Constructing λ-Angenent curve. method Modified curve shortening flow
result Constructs λ-Angenent curve. We develop a machine learning approach to represent and analyze the underlying spatial structure that governs shot selection among professional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. T…
Research suggests using deep learning for better recommendation systems.
problem Recommender systems rely on proxies for A/B testing, leading to random success.
method Advocates for using deep learning to improve recommendation performance.
result Deep learning can potentially optimize reward in recommendation systems.
Develops a machine learning framework for computing most probable paths in stochastic systems.
problem Computing the most probable paths in stochastic dynamical systems.
method Reformulates the boundary value problem of Hamiltonian systems and uses a neural network to solve the Euler-Lagrange equation for the Onsager-Machlup action functional.
result Demonstrates the efficacy and accuracy of the machine learning approach in computing most probable paths for stochastic systems with various types of noise.
In this paper we show the existence of a closed, embedded λ-hypersurfaces Σ⊂R2n. The hypersurface is diffeomorhic to Sn−1×Sn−1×S1 and exhibits SO(n)×SO(n) symmetry. Our approach uses a "shooting method" similar to the approach used by McG…
Classifies solutions to critical sixth order equations with a singularity.
problem Classifying entire positive singular solutions to critical sixth order equations.
method Integral sliding methods, qualitative analysis of ODEs, topological two-parameter shooting technique.
result Solutions are given by a singular radial factor times a periodic solution to a sixth order IVP with constant coefficients.
TinyBayes detects crop diseases from images on edge devices with high accuracy and minimal resources.
problem Automated disease detection for cocoa crops in resource-constrained settings.
method Combines YOLOv8-Nano for lesion localisation, MobileNetV3-Small for feature extraction, and Jacobi prior for Bayesian classification.
result Achieves 78.7% accuracy on Amini Cocoa Contamination Challenge dataset with 9.5 MB model size and 150 ms inference time.
Gaussian process model learns Hamiltonian systems from noisy data.
problem Learning Hamiltonian systems from long, noisy trajectories.
method Efficient decoupled parameterisation, energy-conserving shooting method.
result Robust inference from short and long trajectories.
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental solution to the sub-Laplacian. This system is known to admit closed orb…
Countries tend to diversify their exports by entering products that are related to their current exports. Yet this average behavior is not representative of every diversification path. In this paper, we introduce a method to identify periods when countries enter unrelated products. We analyze the economic diversificati…
Minimal surfaces in spheres constructed from symmetry reductions of ODEs.
problem Construct minimal surfaces in spheres with symmetry.
method Doubling links of free-boundary minimal cones in R^(p+q+3) with bi-orthogonal symmetry.
result Existence of minimal embeddings of S^p × S^q × S^1 in S^(p+q+2).
Analyzes a critical spherical catenoid in hyperbolic space, proving its index and nullity.
problem Proves the strong form of Medvedev's Morse index conjecture for a specific minimal surface.
method Analytic local resolution via reductions and Sturm shooting-count arguments.
result Analytic local resolution of the strong Medvedev conjecture for the critical spherical catenoid.
This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. to define a Riemannian metric on the space of immersions M'=Imm([0,1],M) by pullback of…
Given an isoparametric function f on the n-dimensional sphere, we consider the space of functions w∘f to reduce the Yamabe equation on the round sphere into a singular ODE on w in the interval [0,π], of the form w"+(h(r)/sinr)w′+λ(∣w∣4/n−2w−w)=0, where h is a monotone function with …
Extended orbit model theory for shape analysis using graded group action framework.
problem Limitations of standard orbit model theory in shape analysis.
method Developed graded group action (GGA) framework with regularity conditions.
result Uniqueness result for momentum map trajectory in multi-scale shape spaces.
An efficient algorithm for Riemannian logarithm on Stiefel manifold family.
problem Efficient computation of Riemannian logarithm on Stiefel manifold for various metrics.
method Generalizes a matrix-algebraic approach for the canonical metric to a one-parameter family of metrics.
result Conserves local linear convergence for the family of metrics.
This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our inaptitude to interconnect both trends as strongly as we wished), it seemed preferable to publish it separately. More factually, our account…
Camera model identification refers to the problem of linking a picture to the camera model used to shoot it. As this might be an enabling factor in different forensic applications to single out possible suspects (e.g., detecting the author of child abuse or terrorist propaganda material), many accurate camera model att…
The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABM) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its 'phase diagram' in the space of parameters. Our first motivation is to understand the lar…
Paper proves Pareto efficient insurance for multiple entities.
problem Optimizing insurance for multiple policyholders and insurers.
method Sum-minimization characterization and pairwise implementability analysis.
result Characterization of Pareto efficient insurance arrangements.
Study of multiplicative connections in Lie groupoids.
problem Defining and understanding multiplicative connections in Lie groupoids.
method Definition and study of multiplicative connections satisfying compatibility with the groupoid structure.
result Identification of the obstruction to the existence of a multiplicative connection.
Study rectifying curves in 3D multiplicative Euclidean space.
problem Investigate rectifying curves in a non-Newtonian geometry setting.
method Apply multiplicative differential-geometric concepts to rectifying curves.
result Classify multiplicative rectifying curves using spherical curves.
The paper classifies symmetric triads with multiplicities and their applications.
problem Classifying symmetric triads with multiplicities and their applications.
method Developed the theory of symmetric triads with multiplicities, classified abstract triads, and determined corresponding triads for commutative compact triads.
result Classified symmetric triads with multiplicities and their applications.
New method identifies proxies for causal effects on multiple outcomes.
problem Estimating causal effects in scenarios with multiple outcomes and treatments.
method Causal discovery method leveraging multiple outcomes as proxies for each treatment effect.
result Parallel studies of multiple outcomes can assist in causal identification.
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. W…
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of n-parallel biquandle operations for any integer n, an…
Study finds methods to learn multiple solutions from single task in offline RL.
problem Learning multiple solutions from a single task in offline RL.
method Proposed algorithms for offline RL.
result Empirical results show learning of multiple solutions in offline RL.
Let (M,ω) be a connected symplectic manifold on which a connected Lie group G acts properly and in a Hamiltonian fashion with moment map $μ:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete cl…
MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
Recently neural networks and multiple instance learning are both attractive topics in Artificial Intelligence related research fields. Deep neural networks have achieved great success in supervised learning problems, and multiple instance learning as a typical weakly-supervised learning method is effective for many app…
X-SHAP assesses multiplicative variable contributions in machine learning models.
problem Understanding multiplicative interactions in machine learning models.
method Model-agnostic method that extends SHAP to assess multiplicative contributions.
result X-SHAP proves useful in capturing multiplicative feature importance.
New infinite-dimensional representations with bounded multiplicity found for Lie groups.
problem Finding representations with bounded multiplicity for Lie groups.
method Proving existence of infinite-dimensional irreducible representations with bounded multiplicity property.
result Infinite-dimensional irreducible representations with bounded multiplicity found for non-compact semisimple Lie groups.
Classifies compact multiplicity free quasi-Hamiltonian manifolds.
problem Classifying compact, multiplicity free, quasi-Hamiltonian manifolds.
method Symplectic reductions and Lie group analysis.
result Recover old and find new examples of these structures.
Paper describes how to extend multiple conjugation quandles using maps.
problem Understanding affine extensions of multiple conjugation quandles.
method Introduces augmented MCQ Alexander pairs for affine extensions.
result Affine extensions of multiple conjugation quandles can be described by quadruples of maps.
New method constructs multiple group racks, differing from known constructions.
problem Define new invariants for spatial surfaces.
method Using a G-family of racks and a normal subgroup N of G.
result New method yields multiple group racks not derived from known methods.
Framework for generating multiple clusterings from multi-view data.
problem Challenges in finding optimal clustering criteria and handling incomplete multi-view data.
method DiMVMC framework that optimizes multiple decoder deep networks to complete data views and generate shared representations.
result DiMVMC outperforms state-of-the-art competitors in generating multiple clusterings with high diversity and quality.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
The paper introduces new measures to quantify variability in decision tree models due to observational multiplicity.
problem The variability in decision tree models due to observational multiplicity.
method Introduces leaf regret and structural regret to decompose observational multiplicity.
result Structural regret is the primary driver of observational multiplicity, accounting for over 15 times the variability of leaf regret in some datasets.
M3E2 neural network estimates multiple treatment effects.
problem Estimating effects of multiple treatments simultaneously.
method Multi-task learning neural network model for multiple treatments, continuous and binary.
result M3E2 outperforms baselines in synthetic datasets.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.