A neural network finds causal relationships among latent variables.
problem Learning causal structure among latent variables in high-dimensional data.
method Redundant Input Neural Network (RINN) with modified architecture and regularized objective function.
result The RINN method successfully recovers latent causal structure between input and output variables.
Electronic Medical Records (EMR) are a rich source of patient information, including measurements reflecting physiologic signs and administered therapies. Identifying which variables are useful in predicting clinical outcomes can be challenging. Advanced algorithms such as deep neural networks were designed to process …
Optimal kernel learning improves GP regression for high-dimensional inputs.
problem High computational costs and low prediction accuracy in GP models with many inputs.
method Approximates GP covariance with a convex combination of kernel functions, identifying active variables.
result Improves prediction accuracy and correctly identifies active input variables.
New method finds sparse groups of input variables for neural networks.
problem Finding optimal groups of input variables for neural networks.
method Developed a new loss function and optimization algorithm for multi-layer non-linear neural networks to achieve group sparsity.
result Achieved group sparsity in three real-world datasets, improving model performance and excluding a significant number of variables.
IANN visualizes all input variables effects simultaneously.
problem Inability to visualize all input variables effects simultaneously in black-box functions.
method Interpretable Architecture Neural Network (IANN) approach.
result Visualization of all input variables effects directly and simultaneously.
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
The paper explains DNNs by quantifying interactions among input variables.
problem Understanding and explaining the complex behavior of deep neural networks.
method The paper defines and quantifies the significance of interactions among multiple input variables using the Shapley value.
result The proposed method effectively explains the behavior of DNNs by assigning attribution values to input variables.
Industrial process control systems try to keep an output variable within a given tolerance around a target value. PID control systems have been widely used in industry to control input variables in order to reach this goal. However, this kind of Transfer Function based approach cannot be extended to complex processes w…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input …
New method reconstructs missing variables in time series using autoencoders and automatic differentiation.
problem Reconstruct missing variables in time series with flexible input and output combinations.
method Train an autoencoder with all features, optimize missing variables as inputs, and use automatic differentiation.
result Flexible input and output combinations can be achieved without retraining the autoencoder.
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables i…
Package provides sensitivity analysis for neural networks.
problem Understanding how input variables affect neural network predictions.
method Partial derivatives method to calculate sensitivities.
result Allows evaluation of variable importance and input-output relationships.
In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained machine learning decision rules, based on their response to the variability of the i…
Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition f…
Improves Bayesian optimisation for engineering design problems with many variables.
problem Efficiently searching for global minima in high-dimensional design spaces.
method Integrates input and output data to identify a reduced latent subspace using probabilistic partial least squares.
result Significant improvements in convergence to the global minimum compared to existing methods.
Derives derivatives and geometric framework for functions with non-independent variables.
problem Characterizing functions with non-independent variables in probabilistic models.
method Derives actual and dependent partial derivatives, dependent Jacobian matrix, and tensor metric.
result Derives gradient, Hessian, and Taylor expansion for functions with non-independent variables.
Two ANOVA-based algorithms boost random Fourier feature models for function approximation.
problem Approximating high-dimensional functions with low-order interactions.
method Utilizes ANOVA decomposition to learn low-order functions and index sets of important variables.
result Significantly reduces approximation error compared to existing methods.
Natural Language Processing models help encode categorical process inputs.
problem Encoding categorical variables in industrial process modeling.
method Using NLP models for categorical variable encoding, combined with dimensionality reduction.
result Meaningful embeddings of categorical variables improve feature importance.
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
VIDON learns operators with variable sensors, overcoming sensor limitations.
problem Fixed sensor locations restrict operator learning applicability.
method Variable-Input Deep Operator Network (VIDON) with random, varying sensors.
result VIDON efficiently approximates operators in PDEs and is robust to sensor permutations.
Neural networks learn faster with correlated latent variables.
problem Efficiently learning from higher-order correlations in neural networks.
method Analytical derivation and simulations of two-layer neural networks.
result Correlations between latent variables speed up learning from higher-order correlations.
WE constructs GP kernels for mixed inputs using weighted EDMs.
problem Limitation of standard GP models in handling categorical variables.
method WEGP constructs kernel function using weighted EDMs for categorical inputs.
result WEGP improves GP model accuracy in both synthetic and real-world optimization problems.
Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition fun…
Unified framework for modeling hierarchical spaces in design problems.
problem Challenges in modeling hierarchical, conditional, heterogeneous, or tree-structured domains.
method Unified framework combining feature modeling and graph theory, introducing meta and partially-decreed variables.
result Demonstrated effectiveness on complex system design problems, including neural networks and green-aircraft.
Traditional medicine typically applies one-size-fits-all treatment for the entire patient population whereas precision medicine develops tailored treatment schemes for different patient subgroups. The fact that some factors may be more significant for a specific patient subgroup motivates clinicians and medical researc…
We develop a method for quantile-based sensitivity analysis in models with discontinuities.
problem Uncertainty in interpreting discontinuous models using traditional derivatives.
method Quantile-based derivatives for discontinuous models with discrete inputs.
result Derivatives of quantile-based outputs are well-defined and provide meaningful insights.
This paper analyzes Mean Decrease Impurity (MDI) variable importance in random forests.
problem Lack of interpretability in random forest variable importances.
method Analysis of Mean Decrease Impurity (MDI) in random forests.
result MDI provides a variance decomposition of the output when variables are independent and there are no interactions.
LatentNN corrects neural network attenuation bias in astronomical data.
problem Neural networks underestimate extreme values due to measurement errors.
method Jointly optimizes network parameters and latent input values.
result LatentNN reduces attenuation bias across various signal-to-noise ratios.
LMGPs extend GPs to handle mixed data, offering better accuracy and interpretability.
problem Handling mixed data types (quantitative and qualitative) in metamodeling.
method Introduce LMGPs that learn a latent manifold for qualitative inputs, using a low-rank linear map.
result LMGPs outperform existing methods in accuracy and versatility.
Study identifies latent variables and models from spacecraft data.
problem Learning reliable models from spacecraft data with complex relationships.
method Inductive bias inspired by controllable canonical forms for sparse, input-dependent latent variables.
result Identifies latent variables up to scaling and determines dynamic models up to transformations for linear and affine systems.
Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for s…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a deep random feature (DRF) expansion model, which makes inference tractable by app…
Prediction and explanation are key objects in supervised machine learning, where predictive models are known as black boxes and explanatory models are known as glass boxes. Explanation provides the necessary and sufficient information to interpret the model output in terms of the model input. It includes assessments of…
We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data …
Paper uses PCE to quantify ML model and input uncertainties.
problem Accurately quantify and propagate combined uncertainties in ML predictions.
method Polynomial Chaos Expansion (PCE) for joint input and model uncertainty.
result Efficient and accurate calculation of output variability and sensitivity.
Proposes a non-convex optimization method for a parsimonious weighted naive Bayes classifier.
problem Improving naïve Bayes classifier performance with a large number of input variables.
method Sparse regularization of model log-likelihood for direct estimation of variable weights.
result Optimization-based weighted naïve Bayes classifiers achieve equivalent performance to averaging-based classifiers.
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of input variables the models naturally counteract the overfitting problem ubiquitous …
Function trees simplify complex ML models for better understanding.
problem Understanding and interpreting machine learning model predictions.
method Representing a multivariate function as a tree of simpler functions.
result Function trees reveal the global internal structure of functions.
Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate…
Proposes a neural network framework for feature selection in high-dimensional settings.
problem Challenges in feature selection and non-linear function estimation in high-dimensional settings.
method Sparse-input neural networks using group concave regularization.
result Establishes finite-sample guarantees for variable selection consistency and prediction accuracy.
Develops fully Bayesian LVGP for better uncertainty quantification.
problem Uncertainty in qualitative inputs for GP models.
method Maps qualitative inputs to latent variables, uses standard GP over LVs, estimates LVs through ML, develops fully Bayesian approach.
result Significant improvements in prediction accuracy and uncertainty quantification over plug-in approach.
SHAFF estimates Shapley effects efficiently even with dependent variables.
problem Challenges in estimating Shapley effects, especially with dependent variables.
method SHAFF uses random forests to estimate Shapley effects efficiently.
result SHAFF provides a fast and accurate estimate of Shapley effects.
Reduces bias in linear models by reweighting samples.
problem Bias in linear models due to collinearity among input variables.
method Sample reweighting to reduce collinearity.
result Improves stability of prediction results across different data distributions.
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.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
Improved covariate shift handling with node-based Bayesian neural networks.
problem Improving generalization under covariate shift in neural networks.
method Introduced node-based Bayesian neural networks that learn latent noise variables to represent input corruptions.
result Node-based BNNs perform well under covariate shift due to input perturbations, improving uncertainty estimation and robustness.
LESS combines local predictors for subsets to learn from heterogeneous input-output pairs.
problem Learning from heterogeneous input-output pairs in populations with varied behavior.
method LESS algorithm: generates subsets, trains local predictors, combines them.
result LESS is highly competitive compared to state-of-the-art methods.