New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
DeepCoDA provides personalized interpretability for complex health data.
problem Interpreting complex health data, especially compositional data, is challenging.
method DeepCoDA framework for high-dimensional compositional data, personalized interpretability through patient-specific weights.
result DeepCoDA maintains state-of-the-art performance and provides coherent, personalized interpretations.
New method for analyzing compositional data, addressing biases in summary statistics.
problem Inadequate effect measures for compositional data, especially in high-dimensionality and sparsity.
method Perturbation-based effect measures, average perturbation effects.
result Proposed estimators efficiently estimate average perturbation effects, outperforming existing techniques.
Adapts Altman's model to compositional data for bankruptcy prediction.
problem Predicting business default using standard financial ratios has issues.
method Uses compositional data methodology with log-ratios and machine learning.
result Compositional methods improve predictive performance, especially random forests.
New sparse GP model learns compositional kernels efficiently.
problem Learning accurate Gaussian Process models with complex kernel structures.
method MultiSVGP model with Horseshoe prior for kernel selection.
result Our model provides better fit and faster computation for large-scale data.
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our framework, samples are generated by sampling components from component generators and fee…
Proposes a new model for clustering multiplex networks with compositional data.
problem Clustering multiplex networks with multiple types of relations and compositional data.
method Multiplex Dirichlet stochastic block model for compositional networks.
result Validated through simulation and applied to international export data.
CFA improves model's ability to generalize across unseen domain-class combinations.
problem Challenges in real-world machine learning applications due to data distribution shifts and limited training data.
method Developed Compositional Feature Alignment (CFA) technique to improve CG ability of pretrained models.
result CFA outperforms common finetuning techniques in compositional generalization.
Diffusion models learn hierarchical composition rules from data.
problem How many samples do generative models need to learn hierarchical composition rules?
method Theoretical and empirical investigation of diffusion models on probabilistic context-free grammars.
result Diffusion models learn hierarchical composition rules with sample complexity scaling polynomially with context size.
This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.
problem Measurement errors in high-dimensional regression models involving compositional covariates.
method Calibration approach for the linear log-contrast model under lenient sparsity conditions.
result Established asymptotic normality of the estimator for inference.
SCL discovers compositional structures in analogical reasoning tasks.
problem Discovering compositional structures in analogical reasoning tasks like Raven's Progressive Matrices.
method Proposes Scattering Compositional Learner (SCL) that composes neural networks in sequence.
result Achieves state-of-the-art performance on RPM datasets with significant improvements.
New findings show disentangled latent representations are not enough for robust compositional generalization.
problem Deep learning models struggle with compositional generalization, especially in out-of-distribution samples.
method Investigated a 2D Gaussian generation task with fully disentangled inputs, then forced disentangled latent representations into full-dimensional output space.
result Forcing disentangled latent representations into full-dimensional output space enables robust compositional generalization.
Memorizing rare examples helps neural networks generalize better.
problem Improving generalization in deep learning models.
method Theoretical analysis and experiments on neural networks with composition capability.
result Memorizing rare examples can help neural networks make correct predictions on rare test examples.
We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on each part, then the second estimator on the outputs of the first estimator. And …
We present new computations of tight shapes obtained using the constrained gradient descent code RIDGERUNNER for 544 composite knots with 12 and fewer crossings, expanding our dataset to 943 knots and links. We use the new data set to analyze two outstanding conjectures about tight knots, namely that the ropelengths of…
A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the α-transformation for compositional data and provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather seemingly complex structure, emplo…
Composite development indicators used in policy making often subjectively aggregate a restricted set of indicators. We show, using dimensionality reduction techniques, including Principal Component Analysis (PCA) and for the first time information filtering and hierarchical clustering, that these composite indicators m…
The paper explores using historical data to improve clinical trial analysis by optimizing covariate weights.
problem Limited covariates in small clinical trials reduce the effectiveness of analysis.
method Leverage historical data to pre-specify covariate weights as a composite covariate.
result A composite covariate improves the cost/benefit ratio and reduces overfitting in small clinical trials.
New filters match advanced composition for adaptive privacy, with practical constants.
problem Limitations of existing adaptive composition methods.
method Constructed new filters and odometers that match advanced composition rates, including constants.
result Achieved fully adaptive privacy with practical filters and odometers.
Sharp privacy bounds for sequential analysis of sensitive data.
problem Privacy degradation under sequential analysis of sensitive data.
method Edgeworth expansion in f-differential privacy framework.
result Improved privacy bounds under composition with refined approximation accuracy.
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and gradually nonconvex composite functions have been adopted to obtain more desirable prop…
New methods for predicting compositional data using conformal prediction.
problem No well-established methods for constructing valid prediction sets in compositional data.
method Investigated three conformal prediction-based approaches for Dirichlet regression models.
result HDR approximation approach is robust in terms of coverage, while grid discretization reduces overcoverage.
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained neural network model is well-crafted for a specific task and targeted to approx…
Bayesian models predict evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models outperform standard benchmarks in forecasting guest origin market shares.
In the past few years, off-policy reinforcement learning methods have shown promising results in their application for robot control. Deep Q-learning, however, still suffers from poor data-efficiency and is susceptible to stochasticity in the environment or reward functions which is limiting with regard to real-world a…
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
Data augmentation improves microbiome disease prediction.
problem Improving predictive models for microbiome data.
method Defined novel data augmentation strategies for simplex-valued data.
result Set new state-of-the-art for disease prediction tasks.
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite likelihood approach using a general belief updating framework, which leads to a recu…
Improved subgradient method tackles ill-conditioned composite optimization problems.
problem Slow convergence of subgradient method for composite optimization problems.
method Preconditioned subgradient method with Levenberg-Marquardt approach.
result Linear convergence rate for composite optimization problems under mild conditions.
This paper analyzes how diffusion models learn and generalize concepts.
problem Learning and generalizing concepts in compositional data-generating processes.
method Introduced a structured identity mapping (SIM) task to analyze neural network learning dynamics.
result SIM task captures key empirical observations on compositional generalization.
Three supervised learning methods for selecting logratios in compositional data analysis.
problem Selecting logratios for predicting a dependent variable in compositional data.
method Three supervised learning methods: unrestricted search, parts restriction, and additive logratios.
result The first method excels in predictive power, while the other two are more interpretable.
Bayesian model predicts evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models achieve lower forecast error and competitive performance in guest origin market shares.
With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a…
CTLNet predicts Shanghai Composite Index with improved accuracy.
problem Predicting Shanghai Composite Index for investors and researchers.
method Proposes CNN-Transformer-LSTM Networks (CTLNet) for multivariate time series forecasting.
result CTLNet outperforms state-of-the-art baselines in Shanghai Composite Index prediction.
JIMA uses multi-level preference data to recommend composite items.
problem Recommending composite items efficiently with multi-level preference information.
method Joint Interaction Modeling (JIMA) approach that integrates multi-level preference data and interactions.
result JIMA outperforms advanced baselines in offline and online settings.
New financial ratios using compositional data improve analysis of firm health.
problem Statistical issues with standard financial ratios, especially skewness and outliers.
method Compositional data (CoDa) methodology to analyze financial statements.
result Outliers and skewness reduced, results invariant to numerator and denominator permutation.
Optimizes natural frequencies of cellular composites with various microstructures.
problem Designing cellular composites with diverse microstructures for maximizing natural frequencies.
method Data-driven topology optimization with a latent-variable Gaussian process model.
result Cellular designs with multiclass microstructures achieve higher natural frequencies.
Conventional sequential learning methods such as Recurrent Neural Networks (RNNs) focus on interactions between consecutive inputs, i.e. first-order Markovian dependency. However, most of sequential data, as seen with videos, have complex dependency structures that imply variable-length semantic flows and their composi…
Generative model improves scene graph prediction for rare compositions.
problem Challenges in inferring unseen or rare scene graph compositions.
method Synthesizing rare scene graphs by perturbing real ones, using conditional GANs.
result Marginal but consistent improvements in zero- and few-shot metrics.