CCI algorithm handles cycles, latent variables, and selection bias in causal discovery.
problem Cycles, latent variables, and selection bias in causal processes.
method CCI algorithm using a conditional independence oracle for cyclic, latent, and selection bias cases.
result CCI outperforms existing algorithms in cyclic cases and rivals them in acyclic cases.
We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient space grows fast…
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
Researchers compute bounds and formulas for non-orientable 4-genus of torus knots.
problem Measuring the minimum genus of non-orientable surfaces bounded by torus knots.
method Computed bounds and provided a generalized formula for non-orientable 4-genus of torus knots.
result Computed bounds and a generalized formula for non-orientable 4-genus of torus knots.
In this paper, we introduce a novel, non-recursive, maximal matching algorithm for double auctions, which aims to maximize the amount of commodities to be traded. It differs from the usual equilibrium matching, which clears a market at the equilibrium price. We compare the two algorithms through experimental analyses, …
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
BBRT improves molecular properties through iterative translation.
problem Optimizing molecular structures for improved biochemical properties.
method Iterative translation of molecules using a black box approach.
result Improvement in molecular properties with each iteration of the translator.
Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
New invariants derived from Seifert graphs help distinguish alternating links.
problem Distinguishing alternating links from each other.
method Introducing new quantities derived from Seifert graphs of reduced alternating link diagrams and proving they are link invariants.
result These new invariants can easily distinguish many different alternating links, even large and complicated ones.
In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the relevant information of the nonlinear system is captured by an unknown state vecto…
Analyzes neural networks using linear models to understand their behavior.
problem Understanding multi-layer neural networks through linear models.
method Recalls and reviews four models: linear regression with concentrated features, kernel ridge regression, random feature model, and neural tangent model.
result Highlights limitations of linear theory and discusses approaches to overcome them.
Unified derivation of high-dimensional linear models using stochastic gradient descent.
problem Performance analysis of high-dimensional linear models trained with stochastic gradient descent.
method Derivation of a deterministic equivalence for the two-point function of a random matrix resolvent.
result Unified understanding of model performance including previously known and novel results.
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…
BELIEF framework interprets GLMs using binary linear models.
problem Understanding and interpreting generalized linear models (GLMs) with binary outcomes.
method Developed a framework called binary expansion linear effect (BELIEF) to interpret GLMs through transparent linear models.
result BELIEF framework reveals perfect predictors in complete separation scenarios.
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the Gaussian processes which encode the linear model either have probability of nearly…
PILOT is a fast algorithm for linear model trees that outperforms existing methods.
problem Fitting linear model trees to large datasets efficiently and accurately.
method Greedy training with L2 boosting and model selection rule. result PILOT outperforms standard decision trees and other linear model trees on various datasets.
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …
Analyzes generalization error in generalized linear models, explaining double descent phenomenon.
problem Understanding generalization of machine learning models in high dimensions.
method Develops a framework to characterize asymptotic generalization error for generalized linear models.
result Rigorously explains the double descent phenomenon in generalized linear models.
RGAM builds more accurate models by preferring linear features over non-linear ones.
problem Building accurate models when linearity assumption is poor.
method Multi-stage algorithm guided by the principle of preferring linear features.
result RGAM can fit sparse generalized additive models at scale for various data types.
New approach improves linear-time attention for language models.
problem Challenges of quadratic attention in long-sequence modelling, especially for discrete data.
method Reinterpreting linear attention through latent probabilistic graphical models, introducing asymmetric structure and recurrent parameterisation.
result Our model achieves competitive performance and outperforms existing linear attention variants on language modelling benchmarks.
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.
LoLCATs improves linearized LLM quality with less memory and compute.
problem Linearizing large language models (LLMs) often degrades model quality and requires expensive training.
method Two-step method: attention transfer and low-rank adaptation.
result Significant improvement in linearizing quality with 20+ points on 5-shot MMLU.
LQF linearizes deep models for better interpretability.
problem Lack of interpretability in deep neural networks.
method Simple modifications to architecture, loss function, and optimization.
result Comparable performance to non-linear fine-tuning, with interpretability.
Improved electricity price forecasting model combining linear and non-linear structures.
problem Day-ahead electricity price forecasting in energy systems.
method Recurrent neural networks with embedded linear structures.
result Approximately 11% higher accuracy than state-of-the-art models.
Quadratic memory needed for linear prediction in streaming model.
problem Scalable memory-efficient linear prediction in streaming model.
method Memory lower bound for finding orthogonal vectors and estimates on Grassmannian packing.
result Problems cannot be solved by scalable memory-efficient streaming algorithms.
Improved few-shot learning with interpretable models.
problem Few-shot learning with limited data.
method Linear Distillation Learning using linear functions for each class.
result Better performance compared to other interpretable models.
Efficient algorithm for conditional linear regression.
problem Building models that accurately predict a specific segment of data.
method Efficient algorithm for identifying a significant segment of the population and its linear regression fit.
result Theoretical analysis and efficient algorithm for conditional linear regression.
Python library automates feature engineering and selection for linear models.
problem Difficulties in training and explaining complex machine learning models.
method Automated feature engineering and selection for linear models.
result Improves prediction accuracy of linear models while retaining interpretability.
Review of privacy-preserving linear models for high-dimensional data.
problem Overfitting and data memorization in high-dimensional linear models.
method Comprehensive comparison of optimization techniques for differentially private high-dimensional linear models.
result Coordinate-optimized algorithms perform best in empirical tests.
StarNet trains deep models without gradients using linear equations.
problem Training deep generative models with gradients.
method Solving determined systems of linear equations.
result Least-square bounds for latent codes and model parameters.
This work explains how linear representations in large language models arise from training objectives and gradient descent.
problem Understanding the origins of linear representations in large language models.
method A latent variable model to abstract and formalize concept dynamics, combined with analysis of the softmax cross-entropy objective and gradient descent.
result Linear representations emerge when learning from data matching the latent variable model, and this simple structure suffices to yield linear representations.
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predict…
Proposes a deep learning model to improve stock market prediction.
problem Lack of interpretability in linear multi-factor models for stock prediction.
method Extends linear multi-factor model to LSTM+LRP for non-linear and time-varying predictions.
result Deep recurrent factor model outperforms traditional models in predictive capability.
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.
Optimizes explanations for linear models to enhance trust and interpretability.
problem Lack of well-defined interpretability for linear models and ad hoc approaches.
method Optimization framework using coordinate updates on coefficients.
result Derives a family of interpretability metrics for linear models.
Develops fast approximations for conditional Shapley values in linear and polynomial models.
problem Estimating conditional Shapley values using regression models is computationally expensive.
method A new approximative estimation method for conditional Shapley values using linear and polynomial regression models.
result Our method significantly reduces computation time compared to existing methods.
The paper analyzes the generalizability of linear autoencoders and multivariate linear regression.
problem Limited theoretical understanding of linear autoencoders' performance.
method Proposes a PAC-Bayes bound for multivariate linear regression and shows LAEs as constrained models.
result The proposed PAC-Bayes bound is tight and correlates with practical metrics.
Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific ind…
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
Contrastive learning helps linear models understand document topics.
problem Document classification with limited labeled data.
method Contrastive learning applied to document topic modeling.
result Linear models can recover topic posterior information from contrastive learning representations.
A new decision tree variant improves linear model performance.
problem Improving decision tree performance on non-linear data.
method Extremely random tree with non-linear data transformation and linear observer.
result Outperforms linear models on benchmark dataset.
Dynamic linear models improve travel time prediction for congested freeways.
problem Accurate travel time prediction for congested freeways.
method Dynamic linear models (DLMs) with time-varying parameters.
result Significant improvements in travel time prediction accuracy, especially for short-term predictions.
New method for interpreting non-linear models using forward marginal effects.
problem Interpreting non-linear models' feature effects is challenging.
method Introducing forward marginal effects and partitioning feature space for better interpretation.
result Improved interpretation of non-linear prediction functions.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
Linear regression models are not as interpretable as commonly believed.
problem Interpretability of linear regression models is often overlooked.
method Analysis of common XAI metrics and challenges faced by linear regression models.
result Linear regression models are not inherently interpretable and require careful consideration.
This paper shows neural networks can learn non-linear sparse parities.
problem The challenge of learning non-linear models with neural networks.
method Gradient descent on depth-two neural networks.
result Sparse parities are learnable by neural networks but not by linear methods.
New method solves linear inverse problems using diffusion models.
problem Linear inverse problems in various domains.
method Posterior sampling with latent diffusion models.
result Provable sample recovery in linear models, outperforming previous methods.