Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
This paper explores conditions for neural networks to extrapolate to new domains.
problem Understanding when neural networks can extrapolate to unseen domains.
method Analyzes conditions for nonlinear models to extrapolate under specific distribution shifts.
result Neural networks of the form f(x)=∑fi(xi) can extrapolate if feature covariance is well-conditioned. New techniques identify shifts in financial market sectors.
problem Identifying shifts in financial market structure and composition.
method Developed new mathematical techniques to identify nonlinear shifts in market sectors.
result Identified meaningful sector-to-sector mappings and optimal portfolio styles.
Identifies shifts in causal mechanisms between related datasets using ANMs.
problem Estimating the full causal structure from data is challenging; focus on identifying shifts in causal mechanisms.
method Assumes nonlinear additive noise models, uses Jacobian of score function for mixture distribution to identify shifts.
result Shows applicability of the approach on synthetic and real-world data.
This paper tackles sequential distribution shifts in representation learning.
problem Learning meaningful representations in a sequence of distribution shifts.
method Nonlinear Independent Component Analysis (ICA) framework for continual causal representation learning.
result The method achieves performance comparable to joint training on multiple offline distributions and shows no benefit from the incoming new distribution on all latent variables.
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
This paper extends performative prediction to nonlinear cases.
problem Performative prediction's effectiveness is limited by linear assumptions in real-world applications.
method Formulated a maximum margin approach loss function and extended it to nonlinear spaces using kernel methods.
result Derived conditions for performative stability in both linear and nonlinear cases.
New equivariant filters improve graph classification.
problem Designing deep learning models for graph symmetries.
method Nonlinear spectral filters (NLSFs) that are equivariant to graph functional shifts.
result NLSFs outperform existing spectral GNNs in graph classification.
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes into account (i) the price formation delay between decision and investment by the …
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
problem Analyzing solutions of non-local nonlinear PIDEs in multidimensional spaces.
method Employing abstract semilinear parabolic equations theory in Bessel potential spaces.
result Existence and uniqueness of solutions for a wide class of Lévy measures in multidimensional spaces.
Machine learning detects tipping points in complex systems.
problem Detecting abrupt shifts in complex dynamical systems.
method Equilibrium-informed neural networks (EINNs) trained on candidate equilibrium states.
result EINNs can identify critical thresholds in nonlinear systems.
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
Framework LiLY recovers latent causal variables from time-series data under distribution shifts.
problem Learning and correcting models under unknown distribution shifts in time-series data.
method LiLY framework that recovers latent causal variables and identifies their relations from temporal data under different distribution shifts.
result The framework reliably identifies time-delayed latent causal influences from observed variables under different distribution changes.
The paper proves rigidity for hypersurfaces with constant shifted curvature functions in warped product manifolds.
problem Characterizing and proving rigidity for hypersurfaces with constant shifted curvature functions.
method Using integral inequalities and Minkowski-type formulas, the paper derives rigidity theorems in sub-static warped product manifolds.
result The paper provides new characterizations and rigidity results for hypersurfaces with constant shifted curvature functions in warped product manifolds.
We find a normal form for two-input flat discrete-time systems.
problem No comparable normal form exists for flat continuous-time systems.
method State- and input transformations to achieve a triangular structure.
result A systematic parameterization of system variables by the flat output and its shifts.
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
Boosted Control Functions improve prediction under distributional shifts.
problem Prediction under distributional shifts in the presence of hidden confounding.
method Boosted Control Function (BCF) and ControlTwicing algorithm.
result BCF allows for distribution generalization and invariance under nonlinear, non-identifiable structural functions.
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, …
AdaKoop efficiently models nonlinear dynamics from nonstationary data streams.
problem Capturing nonlinear dynamics in nonstationary data streams with computational efficiency.
method Koopman operator theory and probabilistic framework for streaming data.
result AdaKoop outperforms state-of-the-art methods in real-time forecasting accuracy and efficiency.
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.
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
Proposes a new method for nonlinear models with robustness guarantees.
problem Distributional robustness in nonlinear models with causality.
method Representation learning and identifiable representation learning.
result First causality-inspired robustness method with finite-radius guarantees in nonlinear settings.
The paper tackles exact linearization and control of flat discrete-time systems.
problem Exact linearization and control of flat nonlinear discrete-time systems.
method Investigates conditions for choosing new inputs and feedbacks that may depend on forward-shifts of the new input.
result Easily verifiable conditions for choosing a feasible input and a new input that minimizes forward-shifts of the flat output.
The paper tackles robust classification trees for distribution shifts, improving accuracy in public health and social work.
problem Learning robust classification trees for high-stakes settings with distribution shifts.
method Mixed-integer robust optimization technology to reformulate as a two-stage linear robust optimization problem.
result Increase of up to 12.48% in worst-case accuracy and 4.85% in average-case accuracy.
Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaning…
Transformers learn linear models in-context without updates.
problem Understanding how transformers mimic linear models in-context.
method Gradient flow on linear regression tasks with random initialization.
result Transformers achieve prediction error competitive with best linear predictors.
The article generalizes Pearson correlation to Riemannian manifolds.
problem Analyzing statistical models on non-linear manifolds.
method Reconstitutes Pearson correlation properties and derives a nonlinear generalization.
result Developed the Riemann-Pearson Correlation for manifold analysis.
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random…
ROME improves algorithmic fairness by learning latent group structure robustly.
problem Latent subgroup disparities and distribution shifts in machine learning models.
method ROME uses an Expectation-Maximization algorithm for linear models and a neural Mixture-of-Experts for nonlinear settings.
result ROME significantly improves fairness compared to standard methods while maintaining average performance.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of t…
New deep network derived from rate reduction principles, explaining features and efficiency.
problem Understanding and optimizing deep learning architectures.
method Gradient ascent scheme for rate reduction leading to multi-layer deep network.
result Explicitly constructed multi-layer network with precise optimization and interpretation.
Paper provides a mathematical model for transformer ICL out-of-distribution generalization.
problem Understanding when transformer in-context learning can generalize beyond pre-training data.
method Minimal mathematical model of linear regression tasks with low-rank covariance matrices, analyzing distribution shifts as varying angles between subspaces.
result Transformers can generalize to all angle shifts if pre-training tasks are drawn from a union of subspaces, but not from a single Gaussian.
TTT improves model adaptation to test data, especially for nonlinear models.
problem Improving model performance in adapting to test data, especially for nonlinear models.
method Combining Test-time Training (TTT) with In-context Learning (ICL) for nonlinear models.
result TTT enables models to adapt to both feature vector and link function shifts, improving performance.
Quantum theory reinterprets financial pricing by focusing on observable price transitions.
problem Traditional financial models rely on latent variables; this paper proposes a new observable approach.
method Shift operators, spectral calculus, and Lindblad semigroups are used to define observable frequency operators and convolution generators.
result The framework leads to a nonlocal pricing equation that converges to classical Black-Scholes-Merton under small mesh limits.
New framework TDRL identifies latent causal variables from sequential data.
problem Identify latent causal variables from sequential data.
method Proposes TDRL framework to recover time-delayed latent causal variables and identify their relations from measured sequential data.
result Identifies latent causal variables reliably from sequential data.
MDL principle aids in learning neural network-based causal structures.
problem Learning causal relationships from observations with neural networks.
method Prequential minimum description length (MDL) principle.
result Competitive results on synthetic and real-world data, often recovering correct structure.
Study examines USD exchange rate dynamics using Kramers-Moyal expansion.
problem Understanding and predicting exchange rate instability.
method Kramers-Moyal expansion and Fokker-Planck formalism applied to log-return data.
result Identifies a stabilizing linear drift and nonlinear diffusion term in exchange rate fluctuations.
Scalable methods integrate multiview data for clinical outcomes.
problem Jointly associate and predict outcomes from multiple data sources.
method Randomized Fourier bases for nonlinear mappings, view-independent low-dimensional representations.
result Identified molecular signatures for COVID-19 status and severity.
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
Derives representations invariant under crystallographic groups for functions.
problem Representing and learning functions invariant under crystallographic groups.
method Derives linear and nonlinear representations of functions invariant under crystallographic groups.
result Derives orthonormal crystallographically invariant basis functions and embedding maps.
Study on unknotting twisted knots using arc shift and region arc shift moves.
problem Unknotting twisted knots and finding bounds for region arc shift number.
method Introduced arc shift move and region arc shift move for twisted knots.
result Found families of twisted knots with specific arc shift and region arc shift numbers.
Study detects concept shift in online data using martingales.
problem Detecting concept shift in online datasets.
method Exchangeable martingales and conformal prediction techniques.
result Decomposes concept shift into detectable components.
Study reveals investor heterogeneity in Korean equity market cash flows.
problem Investor heterogeneity and its impact on market dynamics.
method Detrended fluctuation analysis (DFA) on aggregated cash flows.
result Persistence in cash flows varies by investor type, with retail flows showing strong persistence.
Paper proposes SJS model to estimate model performance under covariate and label shifts.
problem Estimating model performance when both covariates and labels shift.
method Sparse Joint Shift (SJS) model and SEES algorithm.
result SEES achieves significant shift estimation error improvements over existing approaches.
Extends FJS analysis to general label spaces, including classification and regression.
problem Distribution shift in general label spaces, including covariate and label shifts.
method Proposes a framework for analyzing FJS in general label spaces and generalizes existing results.
result Generalizes FJS analysis to general label spaces, including classification and regression.
The paper extends IPC framework to stationary physical systems and validates it with a photonic system.
problem Characterizing the computational capabilities of stationary physical systems in a principled, data-efficient way.
method Extended IPC framework, established fundamental results, derived asymptotic bias, introduced data-efficient estimation methods.
result IPC strongly correlates with machine-learning performance and provides a reliable estimate of system dimensionality.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.