Proposes a partially linear structure to capture nonlinear relationships in mixture of experts models.
problem Suboptimal estimates due to linearity assumption in mixture of experts models.
method Introduces a partially linear structure that incorporates unspecified functions to capture nonlinear relationships.
result Establishes the identifiability of the proposed model under mild conditions and introduces a practical estimation algorithm.
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
IDS algorithm optimizes sequential decisions in various monitoring settings.
problem Optimizing sequential decisions in complex monitoring scenarios.
method Information-directed sampling (IDS) algorithm for linear partial monitoring.
result IDS achieves nearly worst-case rate optimality in finite-action games.
Elastic Net improves variable selection in high-dimensional partially linear models.
problem Strongly correlated variables problem in high-dimensional data.
method Proposes Elastic Net procedure for partially linear models.
result Elastic Net better handles correlated variables than other methods.
Flexible DNN for survival data, avoiding proportional hazards assumption.
problem Survival analysis with complex interactions and non-proportional hazards.
method Partially linear DNN model with a flexible nonparametric component.
result FLEXI-Haz achieves optimal convergence rates and asymptotic efficiency.
Algorithm reduces regret in partially observable systems by learning dynamics and using optimistic control.
problem Minimizing regret in partially observable linear quadratic control systems with unknown dynamics.
method ExpCommit algorithm that learns model parameters and uses optimism in uncertainty.
result End-to-end sublinear regret upper bound of O ~ ( T 2 / 3 ) \tilde{\mathcal{O}}(T^{2/3}) O ~ ( T 2/3 ) for ExpCommit. IDS optimizes regret in stochastic partial monitoring with linear rewards.
problem Optimizing decision-making in uncertain environments with linear rewards.
method Information Directed Sampling (IDS) for stochastic partial monitoring.
result Achieves optimal regret rates in all observable game regimes.
New algorithm for distributed learning of sparse partial linear models.
problem Sparse partial linear models in high dimensions with multiple-level structures.
method Debiased distributed learning algorithm based on divide and conquer strategy.
result Global parametric estimator achieves optimal parametric rate in semi-parametric model.
The paper offers methods to estimate and infer the boundary of a set-identified linear model.
problem Estimating and inferring the boundary of a set-identified linear model with many covariates.
method The paper uses semiparametric moment equations and Neyman-orthogonality combined with sample splitting to construct a root-N consistent, uniformly asymptotically Gaussian estimator and a multiplier bootstrap procedure for inference.
result The paper provides a method to estimate and infer the boundary of a set-identified linear model.
Study uses deep neural networks for inference in partially linear models with dependent data.
problem Inference in partially linear models with dependent data.
method First stage deep neural network (DNN) estimation followed by n \sqrt{n} n -consistent and asymptotically normal estimator. result The DNN-estimated finite dimensional parameter achieves n \sqrt{n} n -consistency and asymptotic normality. Linear recurrent networks explain reinforcement learning performance in partially observable settings.
problem Understanding why linear recurrent networks work in reinforcement learning with partial observability.
method Constructed and studied two linear filters for HMMs and action-controlled HMMs.
result Linear filters serve as sufficient statistics and reduce state ambiguity, explaining empirical reinforcement learning success.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
Methodology calculates car insurance premiums for partial damage losses.
problem Estimating premiums for partial damage losses in automobile insurance.
method Used generalized linear models to analyze claim frequency and severity.
result Identified key variables influencing claim frequency and severity.
New method controls linear systems with partial info and disturbances.
problem Controlling linear dynamical systems under partial observation and adversarial disturbances.
method Double Spectral Control (DSC) using two-level spectral approximation strategy.
result Matches best known regret guarantees with exponential runtime improvement.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
KalmanNet uses neural networks to improve state estimation in systems with unknown dynamics.
problem State estimation of systems with non-linear dynamics and partial information.
method KalmanNet integrates a recurrent neural network with the Kalman filter to handle non-linearities and model mismatches.
result KalmanNet outperforms classic filtering methods in systems with both mismatched and accurate domain knowledge.
The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the response. However, the choice of which features to treat as linear or nonlinear is …
A new method combines machine learning with mixed-effects models for better repeated measurement analysis.
problem Inference of linear coefficients in partially linear mixed-effects models with complex interactions and high-dimensional variables.
method Double machine learning approach to estimate nonparametrically nonlinear variables, then use standard linear mixed-effects techniques to estimate the linear coefficient.
result The estimated fixed effects coefficient converges at the parametric rate and is semiparametrically efficient.
PCBM improves neural network generalization by partially observing concepts.
problem Decreased generalization performance due to observing all concepts in CBM.
method Developed a theoretical analysis of PCBM's Bayesian generalization error.
result PCBM's generalization error is lower than CBM's due to partial concept observation.
Proposes new models to recover sparse solutions with partial regularization to mitigate bias.
problem Mitigating bias in sparse recovery solutions.
method Class of models with partial regularizers, showing local/global sparsity properties.
result Models can recover sparsest solutions under certain conditions.
New algorithms solve robust MDPs efficiently, significantly faster than existing methods.
problem Computing robust MDP solutions with uncertainty in transition probabilities is computationally expensive.
method Partial policy iteration and fast robust Bellman operator computation methods.
result The proposed methods are many orders of magnitude faster than state-of-the-art approaches.
The paper addresses nonconvex penalized LAD estimation in partial linear models using DNNs.
problem Challenges in nonconvex penalized LAD estimation with DNNs in partial linear models.
method Parameterizes nonparametric term with DNNs, formulates penalized LAD problem, introduces proximal subgradient method.
result Establishes consistency, convergence rate, and asymptotic normality of the estimator.
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this pa…
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as …
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …
New algorithm estimates partially-observed linear systems with better rates than previous methods.
problem Estimating parameters of partially-observed linear systems with long-term dependencies and semi-parametric noise.
method Prefiltered least squares estimator with semi-parametric noise model.
result First algorithm provably estimates parameters of partially-observed linear systems with rates not dependent on dependency decay rate.
Paper addresses linear regression with partially mismatched data using local search with theoretical guarantees.
problem Linear regression with partially mismatched data.
method Optimization formulation and greedy local search algorithm with theoretical guarantees.
result Local search algorithm converges to nearly-optimal solution at a linear rate under certain conditions.
Paper develops a method for estimating PFLM with minimized rates in high dimensions.
problem Estimating PFLM with minimized rates in high dimensions.
method Least square approach with mixed regularizations of function-norm and ℓ1-norm.
result Established optimal minimax rates of estimation for PFLM.
New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.
problem Limited feedback in sequential learning problems.
method Developed a novel Thompson-sampling-based algorithm to sample from the posterior distribution exactly.
result Achieved logarithmic regret bound of O(log T) for a linearized variant of the problem.
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a …
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
Proposes PLA-GGM for estimating variable associations with confounders.
problem Estimating associations between variables distorted by confounders.
method Partially linear additive Gaussian graphical model (PLA-GGM) with L 1 L_1 L 1 -regularized maximal pseudo-profile likelihood estimator (MaPPLE). result Proves n \sqrt{n} n -sparsistency and superior performance in synthetic and real-world datasets. Study of transitivity in partially hyperbolic maps with expanding linear part.
problem Transitivity of partially hyperbolic endomorphisms with expanding linear part.
method Use of Blichfedt's theorem to analyze dynamical information from homology action.
result Robust transitivity condition and complete dichotomy for special cases.
Study efficient reinforcement learning for partially observed systems with linear structure.
problem Efficient reinforcement learning for partially observed Markov decision processes with linear structure.
method Proposes OP-TENET algorithm using a Bellman operator with finite memory, adversarial integral equation, and optimistic exploration.
result Achieves ε-optimal policy within O(1/ε^2) episodes with polynomial sample complexity in intrinsic dimension.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Proposes a new model to analyze CT scans for lung cancer patients.
problem Analyzing survival risks of lung cancer patients using CT scans.
method Penalized Deep Partially Linear Cox Model (Penalized DPLC) incorporating SCAD penalty and deep neural network.
result The model effectively selects important texture features and estimates nonparametric components.
The paper tackles causal disentanglement with linear models and interventions.
problem Identify latent variables in a causal model from observed data.
method Use linear transformations and interventions to uniquely identify latent variables.
result A single intervention on each latent variable is sufficient for identifying the latent causal model.
AR model forecasts partially observed dynamical time series by estimating evolution function and imputing missing variables.
problem Forecasting dynamical time series with missing variables.
method Autoregressive with slack time series (ARS) model.
result ARS model forecasts future time series with time-invariant and linear assumptions.
New algorithm for partially observable contexts in finance.
problem Decision making based on partially observable, correlated market information.
method EMKF-Bandit algorithm integrating system identification, filtering, and bandit algorithms.
result Sub-linear regret under conditions on filtering.
We tackle linear bandits with partially observable features, achieving sublinear regret.
problem Linear regret due to unobserved features in partially observable linear bandits.
method Feature augmentation with orthogonal basis vectors and a doubly robust estimator.
result Sublinear regret bound of i l d e O ( ( d + d h ) T ) ilde{O}(\sqrt{(d + d_h)T}) i l d e O ( ( d + d h ) T ) . Paper develops efficient Bayesian inference for enzymatic SRNs with LNA metamodel.
problem Bayesian inference for nonlinear SDE-based mechanistic models with partial observations and measurement errors.
method Interpretable Bayesian updating LNA metamodel and efficient posterior sampling.
result Proposed approach demonstrates promising performance in empirical studies.
Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
DPLS improves asset pricing by capturing non-linear risk factor structures.
problem Estimating asset pricing models with non-linear risk factor structures.
method Deep Partial Least Squares (DPLS) for dynamic and flexible factor modeling.
result DPLS models outperform linear models in asset pricing, capturing non-linear risk factor interactions.
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …
Method solves ∂ ˉ \bar\partial ∂ ˉ -harmonic forms on Kodaira-Thurston manifold.
problem Finding ∂ ˉ \bar\partial ∂ ˉ -harmonic forms on Kodaira-Thurston manifold. method Weil-Brezin transform, linear ODE systems, fundamental problem solving.
result Dimension of almost complex ∂ ˉ \bar\partial ∂ ˉ -Hodge numbers can be arbitrarily large. TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.
problem Stochastic linear bandits with partially observed actions in settings like recommendation and healthcare.
method TOFU-POV estimates latent action subspace, imputes missing actions, and runs OFUL in low-dimensional coordinates.
result TOFU-POV achieves T \sqrt{T} T regret scaling with intrinsic subspace dimension, improving upon natural baselines. Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.
problem Understanding the dynamics of absolutely partially hyperbolic surface endomorphisms.
method Showed the existence of a center foliation and leaf conjugacy to the linearization.
result Absolutely partially hyperbolic surface endomorphisms have a dynamically coherent center foliation.