Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several variables simultaneously. In this paper, we present two simple, analytical counterexam…
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48 results for “impossible inference”
New findings show invariance alone isn't enough to identify latent causal variables.
problem Lack of theoretical insights for identifying latent causal variables when variables are latent.
method Assessed the connection between invariance and causal representation learning using impossibility results.
result Invariance alone is insufficient to identify latent causal variables.
Human computation or crowdsourcing involves joint inference of the ground-truth-answers and the worker-abilities by optimizing an objective function, for instance, by maximizing the data likelihood based on an assumed underlying model. A variety of methods have been proposed in the literature to address this inference …
Unified framework improves robust causal inference, overcoming Gaussian barriers and optimization issues.
problem Improving robust causal inference in non-Gaussian settings.
method Combines gamma-Divergence, GNC, and Gatekeeper mechanism.
result Enhanced robustness and global optimization in causal effect estimation.
Adversarial inference on tree models is possible with limited corruption, improving on Kesten-Stigum threshold.
problem Posterior inference on tree-structured graphical models in the presence of adversarial corruption.
method Dynamic programming via belief propagation, constrained adversarial corruption.
result Belief propagation can perform accurate inference with limited adversarial corruption.
Paper proves impossible for large language models to control hallucinations without sacrificing other properties.
problem Achieving truthful knowledge representation, semantic information conservation, and knowledge-constrained optimality simultaneously in large language models.
method Modeling inference as an auction of ideas, using mechanism design, proper scoring rules, and transformer architecture analysis.
result No LLM can simultaneously achieve all four essential properties without violating at least one.
New method warns of counterfactual non-identifiability in DSCMs.
problem Counterfactual inference from observational data is non-identifiable even without unobserved confounding.
method Prove counterfactual identifiability for monotonic generation mechanisms, provide impossibility result for general mechanisms, propose method for estimating worst-case errors.
result Non-identifiability of counterfactual inference from observational data, even in absence of unobserved confounding.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
PriorCVAE uses deep generative models to infer hyperparameters in MCMC.
problem Losing hyperparameter information in GP prior inference.
method Conditioning VAE on hyperparameters to encode and estimate them during inference.
result PriorCVAE enables efficient and distinct inference of hyperparameters.
Theoretical limits show experimental data can falsify but not validate causal estimates from observational studies.
problem Fundamental limits on validating causal estimates using experimental data in observational studies.
method Impossible inference framework, Gaussian Process based approach.
result Experimental data can falsify but not validate causal estimates from observational studies.
Universally valid ground truth is almost impossible to obtain or would come at a very high cost. For supervised learning without universally valid ground truth, a recommended approach is applying crowdsourcing: Gathering a large data set annotated by multiple individuals of varying possibly expertise levels and inferri…
Four-dimensional Einstein Dehn filling is impossible.
problem Complex-hyperbolic Einstein Dehn filling in four dimensions.
method Proof of impossibility.
result Complex-hyperbolic Einstein Dehn filling cannot be performed in dimension four.
This work restricts hidden cardinality in causal models to infer causal relations.
problem Causal relations between variables with a common unobserved cause cannot be directly inferred.
method Derive inequality constraints from d-separation in causal models with known cardinalities of unobserved variables.
result Inference of causal relations is possible with additional assumptions about cardinalities.
Improves probabilistic programming by analyzing program structure.
problem Inefficiency and limitations of single inference algorithms in probabilistic programming.
method Three novel techniques: static and dynamic analyses to adapt programs for more efficient inference.
result Improves probabilistic programming by making inference more efficient.
New method uses path signatures for efficient likelihood estimation in time-series data.
problem Intractable likelihood functions in complex dynamic models.
method Kernel classifier based on path signatures for sequential data.
result Path signatures yield highly performant classifiers, even with low sample numbers.
A new pricing controller handles resource constraints to infer target prices effectively.
problem Resource constraints prevent fixed-price inference, leading to support exclusion.
method Formalizes support-exclusion failure, designs a target-aware controller, and uses a realized information clock.
result The controller can certify feasible target bands and log continuous local densities, leading to polynomial rates of inference.
Machine fairness is impossible to achieve fully due to historical biases.
problem Machine learning models inherit biases from historical data, making it impossible to satisfy fairness metrics simultaneously.
method Presented a causal perspective to the impossibility theorem of fairness.
result It is impossible to satisfy fairness metrics like demographic parity, equal opportunity, and equalized odds simultaneously.
Study functional confounders in causal inference, enabling estimable effects.
problem Causal inference challenges with functional confounders violating positivity.
method Functional interventions, functional positivity, gradient fields, Level-set Orthogonal Descent Estimation (LODE).
result Valid causal effect estimation under certain conditions.
In this article we prove the impossibility of some disentanglement puzzles, first building mathematical models that reflect the essential characteristics of these puzzles.
Transformers mimic Bayesian reasoning in controlled settings, revealing geometric mechanisms.
problem Verifying if transformers perform Bayesian reasoning rigorously in natural data.
method Constructing Bayesian wind tunnels with known posteriors and proving memorization impossibility.
result Transformers achieve - bit accuracy in Bayesian posteriors, while MLPs fail.
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unle…
Study the distribution for low-rank matrix learning, improving inference methods.
problem Lack of understanding of underlying probability distributions in low-rank matrix learning.
method Analyze the distribution , using differential geometry to design an improved MCMC algorithm and learn penalty parameter λ.
result Improved MCMC algorithm and penalty parameter learning for low-rank Bayesian inference.
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven to be more challenging. Here we take a first step towards provable i…
TWM doesn't reduce delta in PDLPs, proving impossibility.
problem TWM in PDLPs doesn't uniformly reduce portfolio delta.
method Proved TWM's condition is self-contradictory and showed impossibility.
result No TWM can uniformly reduce portfolio delta.
New method uses predictions to infer causal effects without labeled data.
problem Data labeling costs limit causal inference experiments.
method Prediction-Powered Causal Inferences (PPCI) using conditional calibration and transfer constraints.
result Valid causal inference achieved on experiments with no human annotations.
An impossibility result shows limitations in learning symmetries and equivariant functions.
problem Learning symmetries and equivariant functions simultaneously is impossible under certain conditions.
method Careful study of approximation for groups and semigroups, analysis of neural networks.
result Linearly equivariant networks can be used to learn equivariant functions, but group-convolutional networks have limitations.
Large language models can't efficiently reason conditionally in a distribution-free setting.
problem Impossibility of conditional PAC-efficient reasoning in large language models.
method Proof of impossibility in a distribution-free setting for non-atomic input spaces.
result Any algorithm achieving conditional PAC efficiency must defer to the expert model with high probability.
No feature ranking can be faithful, stable, and complete when features are collinear.
problem The impossibility of creating a feature ranking that is simultaneously faithful, stable, and complete when features are collinear.
method Proving the impossibility, quantifying it for four model classes, resolving it via ensemble averaging (DASH), and machine-verifying it with Lean 4 theorems.
result No method lies outside the dichotomy of faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods (stable, reporting ties for symmetric features).
Two impossibility theorems show formal alignment certification is impossible for AI systems.
problem Formal certification of AI alignment over open-ended domains is impossible.
method Two independent impossibility theorems: Semantic and Statistical barriers.
result No procedure can simultaneously satisfy soundness, completeness, and tractability.
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
FreB protocol uses AI to infer hidden parameters with valid confidence regions.
problem Generating biased or overconfident conclusions from AI-generated posterior distributions.
method Frequentist-Bayes (FreB) protocol reshapes AI-generated posterior distributions into valid confidence regions.
result FreB provides valid confidence regions that consistently include true parameters with expected probability.
Security, privacy, and fairness have become critical in the era of data science and machine learning. More and more we see that achieving universally secure, private, and fair systems is practically impossible. We have seen for example how generative adversarial networks can be used to learn about the expected private …
A new method for variable importance measures without impossible data.
problem Using impossible data for variable importance measures in black box models.
method Cohort Shapley, a method grounded in economic game theory using only observed data.
result Cohort Shapley provides a more trustworthy explanation of black box models' decisions.
Method scales Bayesian inference to large datasets and robustifies against outliers.
problem Scalability and robustness to outliers in Bayesian inference.
method Variational inference with -divergence and Riemannian coresets.
result Efficiently constructs cleansed data summaries robust to outliers.
Crowdsourcing systems are popular for solving large-scale labelling tasks with low-paid workers. We study the problem of recovering the true labels from the possibly erroneous crowdsourced labels under the popular Dawid-Skene model. To address this inference problem, several algorithms have recently been proposed, but …
Hypersolvers enable fast continuous-depth models for practical applications.
problem Infinite-depth models like Neural ODEs are computationally infeasible for large problems.
method Introducing hypersolvers, neural networks that solve ODEs efficiently with theoretical guarantees.
result Hypersolvers achieve comparable inference time to traditional discrete networks, making continuous-depth models practical.
Far from Asymptopiastat.OT
New optimal prior avoids bias in complex models with limited data.
problem Bias in inference from limited data using Jeffreys prior.
method Developed a principled choice of measure that avoids bias, dependent on data quantity.
result Optimal prior leads to unbiased inference in complex models.
Paper proposes efficient weight updates for edge nodes with minimal communication.
problem Inefficient and resource-intensive full weight updates for edge nodes.
method Deep partial updating, selecting a subset of weights to update.
result Achieves similar performance with fewer weight updates.
The study of tiling homology on flat surfaces, proving impossibility of certain tilings.
problem Proving the non-existence of polyomino tilings on specific square-tiled surfaces.
method Study of homology groups for topological tilings, using coloring proofs.
result Several results about the non-existence of polyomino tilings on certain square-tiled surfaces.
Researchers prove it's impossible to partially recover graph alignments in certain conditions.
problem Recovering vertex correspondence between two random graphs with correlated edges.
method Used the probabilistic method to build automorphisms between tree components of a subcritical Erdös-Rényi graph.
result Proved an impossibility result for partial recovery in the sparse regime with constant average degree and correlation.
New criteria distinguish cause from effect in data, overcoming statistical limitations.
problem Determining causal direction from statistical dependence alone.
method Intuitive criteria based on simplicity of prediction, tested on synthetic data.
result Criteria accurately distinguish cause from effect in various scenarios.
Hass and Scott's example of a 4-valent graph on the 3-punctured sphere that cannot be realized by geodesics in any metric of negative curvature is generalized to impossible configurations filling surfaces of genus with punctures for any and .
The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered structure. Specifically we assume that nodes possess latent attributes drawn from…
This paper develops embeddings that preserve likelihood-based statistical inference.
problem Modern machine learning embeddings destroy the geometric structure required for likelihood-based inference.
method Developed a rigorous theory of likelihood-preserving embeddings and introduced the Likelihood-Ratio Distortion metric.
result Controlling the distortion is necessary and sufficient for preserving inference.
How spiking networks are able to perform probabilistic inference is an intriguing question, not only for understanding information processing in the brain, but also for transferring these computational principles to neuromorphic silicon circuits. A number of computationally powerful spiking network models have been pro…
MSBM extends SB for multi-marginal trajectory inference.
problem Trajectory inference from multiple discrete snapshots.
method Multi-Marginal Schrödinger Bridge Matching (MSBM) using iterative Markovian fitting (IMF).
result MSBM effectively captures complex trajectories and respects intermediate distributions.
New protocol identifies impossible edge orientations in causal graphs.
problem Causal-discovery algorithms cannot distinguish edge directions without assumptions.
method Discrete impossibility certificates and oracle queries.
result Upper bound of expert interactions for DAG recovery.
Develops possibilistic VI using maxitive Donsker-Varadhan formulation.
problem Adapting VI to possibilistic framework to handle uncertainty.
method Maxitive Donsker-Varadhan formulation for possibilistic VI.
result CBOpt optimizers achieve competitive performance in image classification.