One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estima…
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48 results for “nonlinear combinations”
SSMs combined with neural networks match Transformers in dynamic token selection.
problem Understanding the capabilities of SSMs in dynamic token selection.
method Exploring SSMs combined with fully connected neural networks.
result SSMs combined with nonlinear layers can efficiently solve challenging tasks and estimate functions.
JULIA combines multi-linear and nonlinear models for tensor completion.
problem Complex patterns in real-world tensors require a unified model.
method JULIA unifies multi-linear and nonlinear models with flexible component assignment and efficient alternating optimization.
result JULIA outperforms existing methods in large-scale tensor completion.
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of basis functions. We reconstruct the …
Combines Gaussian processes and polynomial chaos for stochastic control.
problem Uncertainties in dynamic models lead to performance issues in predictive control.
method Combines Gaussian processes with polynomial chaos expansions to estimate probability distributions of nonlinear functions.
result Demonstrates accurate approximation and closed-loop performance in stochastic nonlinear model predictive control.
This paper reviews forecast combinations over 50 years, highlighting their evolution and utility.
problem Improving forecast accuracy through combining multiple forecasts.
method Evolution of forecast combination methods, from simple to sophisticated.
result Forecast combinations have become a mainstream approach in forecasting.
New model combines ICA and HMM for unsupervised learning of nonstationary time series.
problem Manual segmentation of non-stationary data is computationally expensive and inaccurate.
method Combines Hidden Markov Model with nonlinear ICA for unsupervised learning.
result Proves identifiability of the model for general mixing nonlinearity.
Many applications in different domains produce large amount of time series data. Making accurate forecasting is critical for many decision makers. Various time series forecasting methods exist which use linear and nonlinear models separately or combination of both. Studies show that combining of linear and nonlinear mo…
A neural network and evolutionary algorithm framework designs nonlinear optical molecules.
problem Designing efficient nonlinear optical materials.
method Multi-stage Bayesian neural network (msBNN) and corrected Lewis-mode group contribution method (cLGC) combined with evolutionary algorithm (EA).
result Accurately and efficiently designs molecules with different optical properties using a small data set.
In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physi…
The paper shows how to recover true node positions from a graph or similarity matrix.
problem Recovering true distances and positions from a graph or similarity matrix.
method Two steps: matrix factorisation followed by nonlinear dimension reduction.
result Nonlinear dimension reduction can recover latent positions close to a manifold where geodesic distance is encoded.
Method estimates parameters of complex nonlinear systems.
problem Parameter estimation for nonlinear systems with derivative states.
method Regularized linear regression using differentiation filtering and least squares.
result Finite-sample bound on mean absolute error of estimation.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our l…
EnKO combines VI and EnKF for efficient latent dynamics inference.
problem Particle degeneracy and biased gradient estimators in SMC-based methods.
method EnKO: hybrid of VI and EnKF.
result EnKO outperforms SMC-based methods in predictive ability and particle efficiency.
Enhances learning of structured distributions using nonlinear denoising score matching.
problem Learning structured distributions from noisy data.
method Latent Nonlinear Denoising Score Matching (LNDSM) integrating nonlinear dynamics with VAE-based latent score matching.
result LNDSM achieves superior sample quality and variability compared to structure-agnostic methods.
In this paper, we introduce a new machine learning (ML) model for nonlinear regression called the Boosted Smooth Transition Regression Trees (BooST), which is a combination of boosting algorithms with smooth transition regression trees. The main advantage of the BooST model is the estimation of the derivatives (partial…
Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We present a novel neurobiologically inspired hierarchical learning framework, Reinfor…
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…
New deep learning model for matrix completion combining linear and nonlinear relationships.
problem Matrix completion considering only linear or nonlinear relations, ignoring latent relationships.
method Combines linear and nonlinear models in a latent variables framework, using a deep neural network with two branches for columns and rows, and manifold learning as an auxiliary task.
result Experimental results show the proposed method outperforms state-of-the-art matrix completion methods.
SOAD model improves data assimilation for nonlinear systems.
problem Challenges in classical data assimilation with high nonlinearity.
method State-Observation Augmented Diffusion (SOAD) model for data-driven assimilation.
result SOAD model matches true posterior distribution under mild assumptions.
Financial Market Dynamicscond-mat.stat-mech
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…
Model-data-driven constitutive responses: application to a multiscale computational frameworkstat.ML
A hybrid method combines model-based and data-driven approaches for multiscale constitutive responses.
problem High computational costs and inaccuracies in nonlinear multiscale methods.
method Hybrid methodology combining model-based constitutive laws, data-driven corrections, and computational multiscale approaches.
result Model-data-driven approach improves macroscale simulations with similar accuracy and computational cost.
A deep learning method solves nonlinear filtering problems efficiently.
problem Nonlinear filtering problem
method Deep splitting method combined with energy-based neural network approximation
result Computational efficiency and performance comparable to Kalman and bootstrap filters
TRNN combines tensor geometry with neural network nonlinearity for HD data.
problem Modeling high-dimensional data with preserved tensor geometry and nonlinear interactions.
method Introduces TRNN that integrates tensor geometry and neural network nonlinearity.
result TRNN preserves tensor geometry while offering nonlinearity.
A new model simulates non-linear adsorption using Gaussian KDEs.
problem Simulating non-linear adsorption processes in porous materials.
method Combines random walk particle tracking with Gaussian Kernel Density Estimators for nonlinear modeling.
result Effective reproduction of Langmuir and Freundlich isotherms.
Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the…
Method estimates bivariate causal models using normalising flows and variational Gaussian process regression.
problem Lack of explainability in AI models, especially in causal mechanisms.
method Combination of normalising flows for density estimation and variational Gaussian process regression for post-nonlinear models.
result Method better explains cause-effect pairs than simple additive noise models.
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert space, giving rise to a complex model where multiple kernels operate on different t…
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
problem Defocusing semilinear wave equations on Schwarzschild spacetime.
method Combining energy and pointwise decay results with Sobolev embedding, constructing scattering operator.
result Construction of a scattering operator mapping past to future scattering data.
Adapts model-based advice to stabilize black-box policies for nonlinear control.
problem Stabilizing machine-learned policies for nonlinear control with limited model information.
method Proposes an adaptive -confident policy to combine black-box and model-based advice.
result Proves the stability of the adaptive -confident policy and its competitive ratio.
Linear quadratic control of nonlinear systems with Koopman operator learning and the Nyström methodmath.OC
Paper uses Koopman operator and Nyström method for efficient nonlinear control.
problem Control of nonlinear dynamical systems.
method Combines Koopman operator framework with Nyström approximation for kernel methods.
result Theoretical guarantees on the convergence rates of the approximated Riccati operator and regulator objective.
Policy Gradient Converges to the Globally Optimal Policy for Nearly Linear-Quadratic Regulatorscs.LG
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is noncompact, constitute a prototype for the formation of singularities, the so-ca…
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this problem via matching the linearly transformed views in a certain latent domain. More…
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
problem Data-efficient nonlinear control in Hamiltonian systems.
method Combines symplectic geometry, recurrence on energy level sets, and chain policies to solve target reachability problems.
result Data requirements depend on geometric and recurrence properties of the Hamiltonian, not the state dimension.
A new model combines VAE and GAN for better anomaly detection in imbalanced datasets.
problem Anomaly detection in imbalanced datasets, especially in medical applications.
method β-VAEGAN model combining VAE and GAN, kernelized SVM for anomaly scores, and deviation from Gaussian prior.
result Improved score from 0.85 to 0.92 on MITBIH Arrhythmia Database.
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolu…
Theory explains deep nonlinear networks' plateaus and transitions.
problem Understanding long plateaus and feature acquisition transitions in deep nonlinear networks.
method Derived an exact identity for Frobenius norms, classified activation functions, and reduced matrix flow to a scalar ODE.
result Escape time law for deep nonlinear networks, where is the number of bottleneck layers.
ATPF combines PF and EnKF for better inference in complex systems.
problem Weight degeneracy in PF and approximation errors in EnKF.
method Adversarial learning to improve posterior matching and incorporate kernel methods for optimization.
result ATPF provides theoretical guarantees and practical advantages over PF and EnKF.
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate the problem (minimising average drawdown, maximum drawdown, or a weighted combi…
New framework for identifying spatial data components using TP latent components.
problem Identifying complex dependencies in spatial data.
method Introduces a new nonlinear ICA framework with -process latent components and develops a learning and inference algorithm.
result Identifiability of TP independent components under general conditions and Gaussian Process limit.
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
New framework for disentangling features from noisy data.
problem Disentangling identifiable features from noisy data.
method Structured Nonlinear Independent Component Analysis (SNICA).
result Identifiability holds even in the presence of noise of unknown distribution.
Enhances kernel regression with network data for better predictions.
problem Improving predictive power in high-dimensional data.
method Combines kernel regression with network cohesion data to model nonlinearities.
result Significantly better predictive performances in high-dimensional data.