Data-Driven Bayesian Network Learning: A Bi-Objective Approach to Address the Bias-Variance Decomposition

Aguilera-Rueda, Vicente-Josué; Cruz-Ramírez, Nicandro; Mezura-Montes, Efrén

doi:10.3390/mca25020037

Cited by 6 publications

(5 citation statements)

References 42 publications

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“…which amounts to computations of function evaluation, constraint evaluation, Jacobian of objective function and the constraint, Hessian of the objective function and the constraint, and the backtracking line search of the step-size. Computing the hypervolume Hessian takes Θ((µn) 3 ) time in addition to the AD-computation of derivatives in Eq. (1).…”

Section: Computational Costmentioning

confidence: 99%

“…For solving Eq. ( 15), we use Cholesky decomposition, which has a computational complexity of O((µ(n + p)) 3 ). It is certainly desired either to have an analytic expression of the HV Hessian or to exploit the block diagonal structure this matrix will certainly have for AD which we, however, have to leave for future research.…”

Section: Computational Costmentioning

confidence: 99%

“…Multi-objective optimization problems (MOPs) -i.e., problems where several objectives have to be optimized concurrently -naturally arise in many applications (e.g., [1][2][3][4]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Wang¹,

Emmerich²,

Deutz³

et al. 2022

Preprint

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Recently, the Hypervolume Newton method (HVN) has been proposed as fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions that are at least twice continuously differentiable. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton-Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily be applied to solve equality constraints with a high precision problems, and to some extend also inequalities. We finally use HVN as local search engine within a MOEA and show the benefit of this hybrid method on several benchmark problems.

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Section: Computational Costmentioning

confidence: 99%

Section: Computational Costmentioning

confidence: 99%

See 1 more Smart Citation

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Wang¹,

Emmerich²,

Deutz³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Some of them apply local approximations with simpler but interpretable models [ 7 ], while others estimate feature importance using permutation techniques [ 8 ]; additionally, they search for influential samples that greatly affect model parameters [ 9 ]. Alternatively, there are methods applied while generating a model that aim to find a trade-off between model accuracy and complexity [ 10 ]. At this stage, optimal sampling techniques or model structures that lead to higher accuracy and lower complexity might be determined [ 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

Post-Analysis of Predictive Modeling with an Epidemiological Example

et al. 2021

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Post-analysis of predictive models fosters their application in practice, as domain experts want to understand the logic behind them. In epidemiology, methods explaining sophisticated models facilitate the usage of up-to-date tools, especially in the high-dimensional predictor space. Investigating how model performance varies for subjects with different conditions is one of the important parts of post-analysis. This paper presents a model-independent approach for post-analysis, aiming to reveal those subjects’ conditions that lead to low or high model performance, compared to the average level on the whole sample. Conditions of interest are presented in the form of rules generated by a multi-objective evolutionary algorithm (MOGA). In this study, Lasso logistic regression (LLR) was trained to predict cardiovascular death by 2016 using the data from the 1984–1989 examination within the Kuopio Ischemic Heart Disease Risk Factor Study (KIHD), which contained 2682 subjects and 950 preselected predictors. After 50 independent runs of five-fold cross-validation, the model performance collected for each subject was used to generate rules describing “easy” and “difficult” cases. LLR with 61 selected predictors, on average, achieved 72.53% accuracy on the whole sample. However, during post-analysis, three categories of subjects were discovered: “Easy” cases with an LLR accuracy of 95.84%, “difficult” cases with an LLR accuracy of 48.11%, and the remaining cases with an LLR accuracy of 71.00%. Moreover, the rule analysis showed that medication was one of the main confusing factors that led to lower model performance. The proposed approach provides insightful information about subjects’ conditions that complicate predictive modeling.

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“…In many applications, we are faced with several conflicting and incommensurable objectives that have to be optimized concurrently (e.g., Reference [1][2][3][4][5]). As a general example, for the design of a certain product, two important objectives are, in most cases, the cost of the product (to be minimized) and its quality (to be maximized), among other possible goals.…”

Section: Introductionmentioning

confidence: 99%

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Cuate

Schütze

2020

Mathematics

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Optimization problems where several objectives have to be considered concurrently arise in many applications. Since decision-making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known as many objective optimization problems (MaOPs). For such problems, it is not possible any more to compute finite size approximations that suitably represent the entire solution set. If no users preferences are at hand, so-called knee points are promising candidates since they represent at least locally the best trade-off solutions among the considered objective values. In this paper, we extend the global/local exploration tool Pareto Explorer (PE) for the detection of such solutions. More precisely, starting from an initial solution, the goal of the modified PE is to compute a path of evenly spread solutions from this point along the Pareto front leading to a knee of the MaOP. The knee solution, as well as all other points from this path, are of potential interest for the underlying decision-making process. The benefit of the approach is demonstrated in several examples.

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Data-Driven Bayesian Network Learning: A Bi-Objective Approach to Address the Bias-Variance Decomposition

Cited by 6 publications

References 42 publications

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

The Hypervolume Newton Method for Constrained Multi-objective Optimization Problems

Post-Analysis of Predictive Modeling with an Epidemiological Example

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

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