Search: intractable - ai.jp.net

research #timeseries 🔬 ResearchAnalyzed: Jan 5, 2026 09:55

Deep Learning Accelerates Spectral Density Estimation for Functional Time Series

Published:Jan 5, 2026 05:00

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1 min read

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ArXiv Stats ML

Analysis

This paper presents a novel deep learning approach to address the computational bottleneck in spectral density estimation for functional time series, particularly those defined on large domains. By circumventing the need to compute large autocovariance kernels, the proposed method offers a significant speedup and enables analysis of datasets previously intractable. The application to fMRI images demonstrates the practical relevance and potential impact of this technique.

Key Takeaways

•Proposes a deep learning estimator for spectral density of functional time series.
•Avoids computation of large autocovariance kernels, enabling faster computation.
•Validated with simulations and application to fMRI images.

Reference

“Our estimator can be trained without computing the autocovariance kernels and it can be parallelized to provide the estimates much faster than existing approaches.”

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Research Paper #Dynamical Systems, Bayesian Inference, Parameter Estimation, Uncertainty Quantification 🔬 ResearchAnalyzed: Jan 3, 2026 06:11

Online Parameter-State Estimation with Uncertainty Quantification via Variational Inference

Published:Dec 31, 2025 18:52

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1 min read

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ArXiv

Analysis

This paper addresses the critical problem of online joint estimation of parameters and states in dynamical systems, crucial for applications like digital twins. It proposes a computationally efficient variational inference framework to approximate the intractable joint posterior distribution, enabling uncertainty quantification. The method's effectiveness is demonstrated through numerical experiments, showing its accuracy, robustness, and scalability compared to existing methods.

Key Takeaways

•Proposes a variational inference framework for online parameter-state estimation.
•Provides uncertainty quantification through approximation of the joint posterior.
•Demonstrates accuracy, robustness, and scalability through numerical experiments.
•Outperforms existing methods in certain scenarios.

Reference

“The paper presents an online variational inference framework to compute its approximation at each time step.”

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Research Paper #Bayesian Statistics, Elastic Net, Regression, Machine Learning 🔬 ResearchAnalyzed: Jan 3, 2026 06:12

Bayesian Elastic Net with Structured Prior Dependence

Published:Dec 31, 2025 18:41

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1 min read

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ArXiv

Analysis

This paper addresses a limitation in Bayesian regression models, specifically the assumption of independent regression coefficients. By introducing the orthant normal distribution, the authors enable structured prior dependence in the Bayesian elastic net, offering greater modeling flexibility. The paper's contribution lies in providing a new link between penalized optimization and regression priors, and in developing a computationally efficient Gibbs sampling method to overcome the challenge of an intractable normalizing constant. The paper demonstrates the benefits of this approach through simulations and a real-world data example.

Key Takeaways

•Addresses the limitation of independent regression coefficients in Bayesian regression.
•Introduces the orthant normal distribution to enable structured prior dependence.
•Provides a new link between penalized optimization and regression priors.
•Develops a computationally efficient Gibbs sampling method.
•Demonstrates benefits through simulation and a real-world example.

Reference

“The paper introduces the orthant normal distribution in its general form and shows how it can be used to structure prior dependence in the Bayesian elastic net regression model.”

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Research Paper #Graph Theory, Parameterized Complexity, Fair Division 🔬 ResearchAnalyzed: Jan 3, 2026 06:13

Parameterized Complexity of Fair Orientations in Graphs

Published:Dec 31, 2025 18:30

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1 min read

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ArXiv

Analysis

This paper investigates the computational complexity of finding fair orientations in graphs, a problem relevant to fair division scenarios. It focuses on EF (envy-free) orientations, which have been less studied than EFX orientations. The paper's significance lies in its parameterized complexity analysis, identifying tractable cases, hardness results, and parameterizations for both simple graphs and multigraphs. It also provides insights into the relationship between EF and EFX orientations, answering an open question and improving upon existing work. The study of charity in the orientation setting further extends the paper's contribution.

Key Takeaways

•Introduces the study of EF orientations in graphs.
•Applies parameterized complexity analysis to identify tractable and intractable cases.
•Provides results for both simple graphs and multigraphs.
•Answers an open question regarding the structural parameterized complexity of EFX orientations.
•Considers charity in the orientation setting, establishing algorithms for finding the minimum amount of edges to remove for EF(X) orientations to exist.

Reference

“The paper initiates the study of EF orientations, mostly under the lens of parameterized complexity, presenting various tractable cases, hardness results, and parameterizations.”

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Research Paper #Bioinformatics, Genome Rearrangement, Approximation Algorithms 🔬 ResearchAnalyzed: Jan 3, 2026 06:14

Approximations for Genome Rearrangement Distance

Published:Dec 31, 2025 18:06

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1 min read

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ArXiv

Analysis

This paper addresses the problem of calculating the distance between genomes, considering various rearrangement operations (reversals, transpositions, indels), gene orientations, intergenic region lengths, and operation weights. This is a significant problem in bioinformatics for comparing genomes and understanding evolutionary relationships. The paper's contribution lies in providing approximation algorithms for this complex problem, which is crucial because finding the exact solution is often computationally intractable. The use of the Labeled Intergenic Breakpoint Graph is a key element in their approach.

Key Takeaways

Reference

“The paper introduces an algorithm with guaranteed approximations considering some sets of weights for the operations.”

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Research Paper #Quantum Computing, Optimization, QAOA, MaxCut, Barren Plateaus 🔬 ResearchAnalyzed: Jan 3, 2026 08:54

QAOA Suffers from Barren Plateaus for Most MaxCut Instances

Published:Dec 31, 2025 03:02

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1 min read

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ArXiv

Analysis

This paper investigates the trainability of the Quantum Approximate Optimization Algorithm (QAOA) for the MaxCut problem. It demonstrates that QAOA suffers from barren plateaus (regions where the loss function is nearly flat) for a vast majority of weighted and unweighted graphs, making training intractable. This is a significant finding because it highlights a fundamental limitation of QAOA for a common optimization problem. The paper provides a new algorithm to analyze the Dynamical Lie Algebra (DLA), a key indicator of trainability, which allows for faster analysis of graph instances. The results suggest that QAOA's performance may be severely limited in practical applications.

Key Takeaways

•QAOA suffers from barren plateaus for most MaxCut instances, making training difficult.
•The DLA dimension grows exponentially for a large fraction of graphs.
•A new algorithm is developed to analyze the DLA, improving computational efficiency.
•The findings suggest limitations in QAOA's practical applicability for MaxCut.

Reference

“The paper shows that the DLA dimension grows as $Θ(4^n)$ for weighted graphs (with continuous weight distributions) and almost all unweighted graphs, implying barren plateaus.”

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Research Paper #Network Science, Machine Learning, Graph Neural Networks 🔬 ResearchAnalyzed: Jan 3, 2026 18:35

Information Localization in Growing Networks

Published:Dec 29, 2025 17:27

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1 min read

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ArXiv

Analysis

This paper introduces the concept of information localization in growing network models, demonstrating that information about model parameters is often contained within small subgraphs. This has significant implications for inference, allowing for the use of graph neural networks (GNNs) with limited receptive fields to approximate the posterior distribution of model parameters. The work provides a theoretical justification for analyzing local subgraphs and using GNNs for likelihood-free inference, which is crucial for complex network models where the likelihood is intractable. The paper's findings are important because they offer a computationally efficient way to perform inference on growing network models, which are used to model a wide range of real-world phenomena.

Key Takeaways

•Information about model parameters in growing network models is often localized.
•This localization allows for efficient inference using GNNs with limited receptive fields.
•The approach is applicable even for non-localized models, offering a computationally efficient alternative to model-specific inference methods.
•The findings justify the analysis of local subgraphs and the use of GNNs for likelihood-free inference.

Reference

“The likelihood can be expressed in terms of small subgraphs.”

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Research Paper #Artificial Intelligence, Planning, Heuristics 🔬 ResearchAnalyzed: Jan 3, 2026 16:30

Subgoaling Heuristics for Numeric Planning with Infinite Actions

Published:Dec 26, 2025 20:05

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1 min read

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ArXiv

Analysis

This paper addresses the challenge of numeric planning with control parameters, where the number of applicable actions in a state can be infinite. It proposes a novel approach to tackle this by identifying a tractable subset of problems and transforming them into simpler tasks. The use of subgoaling heuristics allows for effective goal distance estimation, enabling the application of traditional numeric heuristics in a previously intractable setting. This is significant because it expands the applicability of existing planning techniques to more complex scenarios.

Key Takeaways

•Addresses the challenge of infinite actions in numeric planning.
•Proposes a compilation approach to simplify complex problems.
•Utilizes subgoaling heuristics for goal distance estimation.
•Extends the applicability of traditional numeric heuristics.

Reference

“The proposed compilation makes it possible to effectively use subgoaling heuristics to estimate goal distance in numeric planning problems involving control parameters.”

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Research Paper #Simulation-Based Inference, Diffusion Models, Machine Learning, Scientific Computing 🔬 ResearchAnalyzed: Jan 3, 2026 16:31

Diffusion-based Simulation-Based Inference: A Review

Published:Dec 26, 2025 18:18

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1 min read

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ArXiv

Analysis

This paper provides a comprehensive review of diffusion-based Simulation-Based Inference (SBI), a method for inferring parameters in complex simulation problems where likelihood functions are intractable. It highlights the advantages of diffusion models in addressing limitations of other SBI techniques like normalizing flows, particularly in handling non-ideal data scenarios common in scientific applications. The review's focus on robustness, addressing issues like misspecification, unstructured data, and missingness, makes it valuable for researchers working with real-world scientific data. The paper's emphasis on foundations, practical applications, and open problems, especially in the context of uncertainty quantification for geophysical models, positions it as a significant contribution to the field.

Key Takeaways

•Reviews diffusion-based SBI, a method for likelihood-free inference.
•Highlights the use of diffusion models for posterior sampling.
•Addresses robustness in non-ideal data scenarios (misspecification, unstructured data, missingness).
•Discusses open problems and applications in uncertainty quantification for geophysical models.

Reference

“Diffusion models offer a flexible framework for SBI tasks, addressing pain points of normalizing flows and offering robustness in non-ideal data conditions.”

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Research #llm 🔬 ResearchAnalyzed: Dec 25, 2025 04:07

Semiparametric KSD Test: Unifying Score and Distance-Based Approaches for Goodness-of-Fit Testing

Published:Dec 24, 2025 05:00

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1 min read

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ArXiv Stats ML

Analysis

This arXiv paper introduces a novel semiparametric kernelized Stein discrepancy (SKSD) test for goodness-of-fit. The core innovation lies in bridging the gap between score-based and distance-based GoF tests, reinterpreting classical distance-based methods as score-based constructions. The SKSD test offers computational efficiency and accommodates general nuisance-parameter estimators, addressing limitations of existing nonparametric score-based tests. The paper claims universal consistency and Pitman efficiency for the SKSD test, supported by a parametric bootstrap procedure. This research is significant because it provides a more versatile and efficient approach to assessing model adequacy, particularly for models with intractable likelihoods but tractable scores.

Key Takeaways

Reference

“Building on this insight, we propose a new nonparametric score-based GoF test through a special class of IPM induced by kernelized Stein's function class, called semiparametric kernelized Stein discrepancy (SKSD) test.”

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Technology #Artificial Intelligence 🏛️ OfficialAnalyzed: Jan 3, 2026 09:40

Introducing AI stories: daily benefits shine a light on bigger opportunities

Published:May 6, 2025 10:30

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1 min read

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OpenAI News

Analysis

The article highlights the potential of AI to solve major global problems and usher in an era of unprecedented progress. It focuses on the optimistic vision of AI's impact, emphasizing its ability to make the seemingly impossible, possible.

Key Takeaways

•AI is poised to solve major global problems.
•The article presents an optimistic view of AI's potential.
•The Intelligence Age is characterized by AI's ability to enhance human capabilities.

Reference

“Sam Altman has written that we are entering the Intelligence Age, a time when AI will help people become dramatically more capable. The biggest problems of today—across science, medicine, education, national defense—will no longer seem intractable, but will in fact be solvable. New horizons of possibility and prosperity will open up.”

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Research #AI 📝 BlogAnalyzed: Jan 3, 2026 06:23

An Overview of Deep Learning for Curious People

Published:Jun 21, 2017 00:00

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1 min read

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Lil'Log

Analysis

The article introduces deep learning by referencing the AlphaGo vs. Lee Sedol match, highlighting the significant advancements in AI. It emphasizes the complexity of Go and how AlphaGo's victory marked a turning point in AI's capabilities.

Key Takeaways

•AlphaGo's victory over Lee Sedol in 2016 was a significant event for AI.
•Go's complexity made it a challenging game for computers to master.
•The event highlighted the progress of AI and attracted attention to the field.

Reference

“Before this, Go was considered to be an intractable game for computers to master, as its simple rules lay out an exponential number of variations in the board positions, many more than what in Chess.”

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Deep Learning Accelerates Spectral Density Estimation for Functional Time Series

Analysis

Key Takeaways

Online Parameter-State Estimation with Uncertainty Quantification via Variational Inference

Analysis

Key Takeaways

Bayesian Elastic Net with Structured Prior Dependence

Analysis

Key Takeaways

Parameterized Complexity of Fair Orientations in Graphs

Analysis

Key Takeaways

Approximations for Genome Rearrangement Distance

Analysis

Key Takeaways

QAOA Suffers from Barren Plateaus for Most MaxCut Instances

Analysis

Key Takeaways

Information Localization in Growing Networks

Analysis

Key Takeaways

Subgoaling Heuristics for Numeric Planning with Infinite Actions

Analysis

Key Takeaways

Diffusion-based Simulation-Based Inference: A Review

Analysis

Key Takeaways

Semiparametric KSD Test: Unifying Score and Distance-Based Approaches for Goodness-of-Fit Testing

Analysis

Key Takeaways

Introducing AI stories: daily benefits shine a light on bigger opportunities

Analysis

Key Takeaways

An Overview of Deep Learning for Curious People

Analysis

Key Takeaways

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