Design-by-Analogy (DbA) is a design methodology, wherein new solutions are generated in a target domain based on inspiration drawn from a source domain through cross-domain analogical reasoning [1, 2, 3]. DbA is an active research area in engineering design and various methods and tools have been proposed to support the implement of its process [4, 5, 6, 7, 8]. Studies have shown that DbA can help designers mitigate design fixation [9] and improve design ideation outcomes [10]. Fig.1 presents an example of DbA applications [11]. This case aims to solve an engineering design problem: How might we rectify the loud sonic boom generated when trains travel at high speeds through tunnels in atmospheric conditions [11, 12]? For potential design solutions to this problem, engineers explored structures in other design fields than trains or in the nature that effectively "break" the sonic-boom effect. When looking into the nature, engineers discovered that kingfisher birds could slice through the air and dive into the water at extremely high speeds to catch prey while barely making a splash. By analogy, engineers re-designed the train's front-end nose to mimic the geometry of the kingfisher's beak. This analogical design reduced noise and eliminated tunnel booms.

Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally referred to as decision graphs, and which include decision trees and binary decision diagrams, but also their multi-valued variants, there exist polynomial-time algorithms for computing one PI-explanation. In addition, the paper also proposes a polynomial-time algorithm for computing one contrastive explanation. These novel algorithms build on explanation graphs (XpG's). XpG's denote a graph representation that enables both theoretical and practically efficient computation of explanations for decision graphs. Furthermore, the paper pro- poses a practically efficient solution for the enumeration of explanations, and studies the complexity of deciding whether a given feature is included in some explanation. For the concrete case of decision trees, the paper shows that the set of all contrastive explanations can be enumerated in polynomial time. Finally, the experimental results validate the practical applicability of the algorithms proposed in the paper on a wide range of publicly available benchmarks.

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio, or equivalently the posterior function. We show that this approach can be formulated in terms of mutual information maximization between model parameters and simulated data. We use this equivalence to reinterpret existing approaches for amortized inference, and propose two new methods that rely on lower bounds of the mutual information. We apply our framework to the inference of parameters of stochastic processes and chaotic dynamical systems from sampled trajectories, using artificial neural networks for posterior prediction. Our approach provides a unified framework that leverages the power of mutual information estimators for inference.

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a hierarchical Bayesian model of probabilistic classifier fusion based on a new correlated Dirichlet distribution. This distribution explicitly models positive correlations between marginally Dirichlet-distributed random vectors thereby allowing normative modeling of correlations between base classifiers or experts. The proposed model naturally accommodates the classic Independent Opinion Pool and other independent fusion algorithms as special cases. It is evaluated by uncertainty reduction and correctness of fusion on synthetic and real-world data sets. We show that a change in performance of the fused classifier due to uncertainty reduction can be Bayes optimal even for highly correlated base classifiers.

Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allows optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest is typically assumed to live in some (often unknown) low-dimensional manifold embedded in high-dimensional ambient space. The result is a modelling mismatch since -- by construction -- the invertibility requirement implies high-dimensional support of the learned distribution. Injective flows, mapping from low- to high-dimensional space, aim to fix this discrepancy by learning distributions on manifolds, but the resulting volume-change term becomes more challenging to evaluate. Current approaches either avoid computing this term entirely using various heuristics, or assume the manifold is known beforehand and therefore are not widely applicable. Instead, we propose two methods to tractably calculate the gradient of this term with respect to the parameters of the model, relying on careful use of automatic differentiation and techniques from numerical linear algebra. Both approaches perform end-to-end nonlinear manifold learning and density estimation for data projected onto this manifold. We study the trade-offs between our proposed methods, empirically verify that we outperform approaches ignoring the volume-change term by more accurately learning manifolds and the corresponding distributions on them, and show promising results on out-of-distribution detection.

We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to massive data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP). While sparse approximation methods for GPs and kernel methods share some algebraic similarities, the literature lacks a deep understanding of how and why they are related. This is a possible obstacle for the communications between the GP and kernel communities, making it difficult to transfer results from one side to the other. Our motivation is to remove this possible obstacle, by clarifying the connections between the sparse approximations for GPs and kernel methods. In this work, we study the two popular approaches, the Nystr\"om and SVGP approximations, in the context of a regression problem, and establish various connections and equivalences between them. In particular, we provide an RKHS interpretation of the SVGP approximation, and show that the Evidence Lower Bound of the SVGP contains the objective function of the Nystr\"om approximation, revealing the origin of the algebraic equivalence between the two approaches. We also study recently established convergence results for the SVGP and how they are related to the approximation quality of the Nystr\"om method.

In real world datasets, particular groups are under-represented, much rarer than others, and machine learning classifiers will often preform worse on under-represented populations. This problem is aggravated across many domains where datasets are class imbalanced, with a minority class far rarer than the majority class. Naive approaches to handle under-representation and class imbalance include training sub-population specific classifiers that handle class imbalance or training a global classifier that overlooks sub-population disparities and aims to achieve high overall accuracy by handling class imbalance. In this study, we find that these approaches are vulnerable in class imbalanced datasets with minority sub-populations. We introduced Fair-Net, a branched multitask neural network architecture that improves both classification accuracy and probability calibration across identifiable sub-populations in class imbalanced datasets. Fair-Nets is a straightforward extension to the output layer and error function of a network, so can be incorporated in far more complex architectures. Empirical studies with three real world benchmark datasets demonstrate that Fair-Net improves classification and calibration performance, substantially reducing performance disparity between gender and racial sub-populations.

Recent work proposed $\delta$-relevant inputs (or sets) as a probabilistic explanation for the predictions made by a classifier on a given input. $\delta$-relevant sets are significant because they serve to relate (model-agnostic) Anchors with (model-accurate) PI- explanations, among other explanation approaches. Unfortunately, the computation of smallest size $\delta$-relevant sets is complete for ${NP}^{PP}$, rendering their computation largely infeasible in practice. This paper investigates solutions for tackling the practical limitations of $\delta$-relevant sets. First, the paper alternatively considers the computation of subset-minimal sets. Second, the paper studies concrete families of classifiers, including decision trees among others. For these cases, the paper shows that the computation of subset-minimal $\delta$-relevant sets is in NP, and can be solved with a polynomial number of calls to an NP oracle. The experimental evaluation compares the proposed approach with heuristic explainers for the concrete case of the classifiers studied in the paper, and confirms the advantage of the proposed solution over the state of the art.

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural networks, variational inference is widely used to approximate difficult-to-compute posteriors by variational distributions. Usually, Gaussians are used as variational distributions (Gaussian-VI) which limits the quality of the approximation due to their limited flexibility. Transformation models on the other hand are flexible enough to fit any distribution. Here we present transformation model-based variational inference (TM-VI) and demonstrate that it allows to accurately approximate complex posteriors in models with one parameter and also works in a mean-field fashion for multi-parameter models like neural networks.

Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two key properties: It should be valid (guaranteeing coverage) and discriminative (more uncertain when the expected risk is high). Moreover, when combined with deep learning (DL) methods, it should be scalable and affect the DL model performance minimally. Most existing Bayesian methods lack frequentist coverage guarantees and usually affect model performance. The few available frequentist methods are rarely discriminative and/or violate coverage guarantees due to unrealistic assumptions. Moreover, many methods are expensive or require substantial modifications to the base neural network. Building upon recent advances in conformal prediction and leveraging the classical idea of kernel regression, we propose Locally Valid and Discriminative confidence intervals (LVD), a simple, efficient and lightweight method to construct discriminative confidence intervals (CIs) for almost any DL model. With no assumptions on the data distribution, such CIs also offer finite-sample local coverage guarantees (contrasted to the simpler marginal coverage). Using a diverse set of datasets, we empirically verify that besides being the only locally valid method, LVD also exceeds or matches the performance (including coverage rate and prediction accuracy) of existing uncertainty quantification methods, while offering additional benefits in scalability and flexibility.