The paper identifies generators of linear SDEs with noise types.
problem Identifying the generator of linear SDEs from their solution distribution.
method Deriving sufficient and necessary conditions for additive noise, and sufficient conditions for multiplicative noise.
result Generic conditions for identifying the generator of linear SDEs with both types of noise.
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
The paper shows that certain learned representations are identifiable in function space.
problem Identifiability of learned representations in deep neural networks.
method Using recent advances in nonlinear ICA, the paper shows that a large family of discriminative models are identifiable in function space, up to a linear indeterminacy.
result Many models for representation learning are identifiable in function space, including text, images, and audio.
Linear properties are either universal or absent across language models.
problem Explaining the prevalence of linear properties in language models.
method Proved identifiability of distribution-equivalent next-token predictors and analyzed various notions of linearity.
result Linear properties either hold in all or none distribution-equivalent next-token predictors.
Efficient algorithm for identifying causal effects in linear models.
problem Determining causal effects from observational data under latent confounding.
method Symbolic computation and efficient algorithm for finding identifying formulas.
result Proves the existence of identifying formulas of a specified degree in quasi-polynomial time.
This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.
problem Identifying latent variables in sequential data models.
method Proved identifiability of Markov Switching Models and established conditions for Switching Dynamical Systems.
result Identifiability of latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations.
The paper analyzes identifiability in ODE systems with hidden confounders.
problem Identifiability of ODE systems with hidden confounders.
method Systematic analysis of identifiability in linear ODE systems with hidden confounders, considering both no causal relationships and causal dependencies.
result Comprehensive identifiability analysis of ODE systems with hidden confounders, including causal dependencies.
New models learn stable latent clusters without side info.
problem Stability of non-linear ICA representations without side information.
method Deep generative models with latent clusterings, compared to standard VAEs and auxiliary labeled models.
result Deep generative models with latent clusterings are as stable as models with side information.
Proposes using DII to identify non-linear causal relationships in EU Allowances returns.
problem Identifying causal relationships in non-linear data of EU Allowances returns.
method Uses Differentiable Information Imbalance (DII) for non-parametric causal discovery compared to multivariate Granger causality.
result Significant overlap and differences in causal variables identified by linear and non-linear methods.
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for …
This paper tackles causal representation learning with linear and general transformations.
problem Identify and recover latent causal variables and graphs under unknown transformations.
method Score-based algorithms that use gradients of log-density functions for identifiability and achievability.
result Two stochastic hard interventions per node are sufficient for identifiability of general transformations.
Develops a method to identify causal effects in linear models with latent variables.
problem Identifying causal effects in models with latent variables that are not independent.
method A novel graphical criterion and an integer linear program algorithm.
result Sufficient condition for identifying causal effects by rational formulas in the covariance matrix.
LinFACT identifies all ε-best arms in linear bandits with near-optimal efficiency.
problem Efficiently identifying multiple optimal candidates in high trial-and-error cost tasks.
method LinFACT algorithm designed for linear bandits, with information-theoretic lower bound and upper bound derivation integration.
result LinFACT achieves instance optimality, matching lower bound up to a logarithmic factor.
Paper tackles intervention extrapolation using identifiable representations.
problem Predicting effects of unseen interventions on outcomes.
method Combines identifiable representation learning with autoencoders to enforce linear invariance.
result Identifiable representations enable non-linear extrapolation of interventions.
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
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.
New method identifies causal parameters in tree-shaped linear models using cycles.
problem Identifying causal parameters from correlations in tree-shaped linear models.
method Investigates tree-shaped linear models, uses missing cycles to identify causal parameters, solves quadratic equations.
result Shows how missing cycles can be combined to obtain a unique solution for causal parameters.
New method identifies shared components from unpaired multimodal mixtures.
problem Identify shared components from unpaired multimodal mixtures.
method Distribution divergence minimization-based loss with sufficient conditions for identifiability.
result Sufficient conditions for shared component identifiability from unaligned multimodal mixtures.
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix…
Study robust best-arm identification in linear bandits with lower bounds and algorithms.
problem Identify a near-optimal robust arm in linear bandits with adversarial actions.
method Propose instance-dependent lower bounds and both static and adaptive bandit algorithms.
result Sample complexity matches the lower bound and algorithms effectively identify robust arms.
SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
New method identifies causal relationships from interventions in complex systems.
problem Learning causal representations from unknown, latent interventions with general nonlinear mixing.
method Strong identifiability results with unknown single-node interventions, using geometric structure of transformed data.
result First instance of causal identifiability from non-paired interventions for deep neural network embeddings.
This paper tackles CRL for multi-node interventions, achieving identifiability guarantees.
problem CRL under unknown multi-node interventions, focusing on single-node assumptions.
method Establishes identifiability results for general latent causal models under stochastic interventions.
result Identifiability up to ancestors using soft interventions, perfect identifiability using hard interventions.
The paper accelerates regression algorithms by identifying saturated coordinates.
problem Non-negative and bounded-variable linear regression problems.
method Safe screening technique to identify saturated coordinates.
result The approach provides theoretical guarantees for identifying saturated coordinates.
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without…
This research improves neural network representation identifiability through task structures.
problem Improving neural network representation identifiability in multi-task settings.
method Analyzing the effects of task distributions and causal structures on latent factors, leading to simpler optimization.
result A straightforward optimization procedure enables better representation recovery in both synthetic and real-world data.
Paper proposes a new method to identify causal graphs with latent variables using higher-order cumulants.
problem Estimating causal directed acyclic graphs with latent confounders.
method Uses higher-order cumulants to identify causal structures among observed and latent variables.
result Validates the proposed algorithm through simulations and real-world data.
A point p∈PN of a projective space is h-identifiable, with respect to a variety X⊂PN, if it can be written as linear combination of h elements of X in a unique way. Identifiability is implied by conditions on the contact locus in X of general linear spaces called non weak defecti…
Paper addresses identifiability and asymptotics of ODE systems from noisy data.
problem Identifying parameters and causal structure of linear ODE systems from discrete observations.
method Developed sufficient conditions for identifiability, proved consistency and asymptotic normality of NLS estimator, constructed confidence sets, and inferred causal structure.
result Consistent and asymptotically normal parameter estimator for linear ODE systems under mild conditions.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
We tackle causal discovery in linear systems with measurement error and unobserved causes.
problem Causal discovery in linear systems with measurement error and unobserved causes.
method Characterization of identifiability based on the mixing matrix, proposing causal structure learning methods.
result The structure of causal models can be identified under certain faithfulness assumptions.
Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation. Unlike existing methods, the proposed NGCA algorithm identifies the linear subspac…
We improve robust parameter estimation in causal models from observational data.
problem Robustly estimating parameters in linear structural equation models from observational data.
method Extending Sankararaman et al. (2019) to a broader class of models, providing sufficient conditions for robust identifiability.
result For a large set of parameters, robust identifiability holds and existing algorithms achieve robust identifiability.
Contrastive ICA identifies features in experimental groups relative to controls.
problem Jointly analyzing experimental and control datasets to identify salient features.
method Developed contrastive ICA (cICA) using tensor decomposition.
result cICA identifies patterns and visualizes data effectively, outperforming existing methods.
LeJEPA learns latent variables from nonlinear observations.
problem Learning latent variables from nonlinear observations.
method Proves linear identifiability of Gaussian latent distributions.
result Gaussian distribution uniquely guarantees linear identifiability.
This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample s…
Study identifies parameters in causal models with latent confounding.
problem Parameter identification in linear non-Gaussian causal models with latent confounding.
method Graphical criterion for necessary and sufficient identifiability of direct causal effects, with polynomial-time algorithm.
result Developed a graphical criterion for identifying direct causal effects in latent variable models with arbitrary non-linear confounding.
Logit distance bounds representational similarity of models.
problem Approximating linear similarity when distributions are close.
method Defined a logit distance and proved its relationship to representational dissimilarity.
result Logit distance bounds representational similarity, providing nontrivial control in practice.
Improved algorithm for conditional linear regression with heterogeneous covariances.
problem Identifying a linear predictor for a fraction of data with varying covariances.
method Polynomial time algorithm using Disjunctive Normal Form (DNF) to identify a condition and linear predictor.
result Removed requirement for similar covariances in each condition term, improving algorithm applicability.
A new algorithm identifies one of several nearly optimal arms in linear bandits.
problem Identifying one arm that is close to the best arm in linear bandits.
method Developed a procedure to adapt best-arm identification algorithms for ε-best-answer identification in transductive linear stochastic bandits. result Proposed an asymptotically optimal algorithm for ε-best-answer identification. We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
problem Determining the latent dimensions (ranks) in tensor factorization models.
method Prior predictive moment matching to transform moment matching conditions into a log-linear system of equations.
result Identifies which tensor models have identifiable ranks and derives rank estimators.
We identify which latent factors change between environments in linear causal models.
problem Identify latent factors that change between environments in linear causal models with fewer than d interventions. method Propose a method to identify shifted nodes in a smaller number of environments with coarser interventions.
result It is possible to identify the set of shifted nodes under mild assumptions.
We study the theoretical properties of learning a dictionary from N signals xi∈RK for i=1,...,N via l1-minimization. We assume that xi's are i.i.d. random linear combinations of the K columns from a complete (i.e., square and invertible) reference dictionary $\mathbf D_0 \in…
Unpaired multi-domain causal representation learning is possible with sufficient conditions.
problem Learning shared causal representation from unpaired data across domains.
method Identify sufficient conditions for joint distribution and shared causal graph recovery.
result Practical method to recover shared latent causal graph from marginal distributions.
Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε-Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
New method for inference on strongly identified functionals even when nuisance functions are weakly identified.
problem Inference on continuous linear functionals of weakly identified nuisance functions defined by conditional moment restrictions.
method Proposes penalized minimax estimators for both the primary and debiasing nuisance functions, which can converge to fixed limits regardless of nuisance identifiability.
result Proves the asymptotic normality of a debiased estimator for the functional of interest, leading to asymptotically valid confidence intervals.