In this paper, we address the task of characterizing the chemical composition of planetary surfaces using convolutional neural networks (CNNs). Specifically, we seek to predict the multi-oxide weights of rock samples based on spectroscopic data collected under Martian conditions. We frame this problem as a multi-target regression task and propose a novel regularization method based on f-divergence. The f-divergence regularization is designed to constrain the distributional discrepancy between predictions and noisy targets. This regularizer serves a dual purpose: on the one hand, it mitigates overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets. On the other hand, it acts as an auxiliary loss function, penalizing the neural network when the divergence between the predicted and target distributions becomes too large. To enable backpropagation during neural network training, we develop a differentiable f-divergence and incorporate it into the f-divergence regularization, making the network training feasible. We conduct experiments using spectra collected in a Mars-like environment by the remote-sensing instruments aboard the Curiosity and Perseverance rovers. Experimental results on multi-oxide weight prediction demonstrate that the proposed $f$-divergence regularization performs better than or comparable to standard regularization methods including $L_1$, $L_2$, and dropout. Notably, combining the $f$-divergence regularization with these standard regularization further enhances performance, outperforming each regularization method used independently.
The selection of algorithms is a crucial step in designing AI services for real-world time series classification use cases. Traditional methods such as neural architecture search, automated machine learning, combined algorithm selection, and hyperparameter optimizations are effective but require considerable computational resources and necessitate access to all data points to run their optimizations. In this work, we introduce a novel data fingerprint that describes any time series classification dataset in a privacy-preserving manner and provides insight into the algorithm selection problem without requiring training on the (unseen) dataset. By decomposing the multi-target regression problem, only our data fingerprints are used to estimate algorithm performance and uncertainty in a scalable and adaptable manner. Our approach is evaluated on the 112 University of California riverside benchmark datasets, demonstrating its effectiveness in predicting the performance of 35 state-of-the-art algorithms and providing valuable insights for effective algorithm selection in time series classification service systems, improving a naive baseline by 7.32% on average in estimating the mean performance and 15.81% in estimating the uncertainty.
Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized yet well-distributed models that collectively embody different trade-offs in one algorithmic pass, this paper proposes to view Pareto multi-task learning through the lens of multi-task optimization. Multi-task learning is first cast as a multi-objective optimization problem, which is then decomposed into a diverse set of unconstrained scalar-valued subproblems. These subproblems are solved jointly using a novel multi-task gradient descent method, whose uniqueness lies in the iterative transfer of model parameters among the subproblems during the course of optimization. A theorem proving faster convergence through the inclusion of such transfers is presented. We investigate the proposed multi-task learning with multi-task optimization for solving various problem settings including image classification, scene understanding, and multi-target regression. Comprehensive experiments confirm that the proposed method significantly advances the state-of-the-art in discovering sets of Pareto-optimized models. Notably, on the large image dataset we tested on, namely NYUv2, the hypervolume convergence achieved by our method was found to be nearly two times faster than the next-best among the state-of-the-art.
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for constructing a high-order polynomial regression based on the Taylor map factorization. This method naturally implements multi-target regression and can capture internal relationships between targets. Additionally, we introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on UCI open access datasets, Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate that the proposed method performs comparable to the state-of-the-art regression methods and outperforms them on specific tasks.
Multi-target regression is useful in a plethora of applications. Although random forest models perform well in these tasks, they are often difficult to interpret. Interpretability is crucial in machine learning, especially when it can directly impact human well-being. Although model-agnostic techniques exist for multi-target regression, specific techniques tailored to random forest models are not available. To address this issue, we propose a technique that provides rule-based interpretations for instances made by a random forest model for multi-target regression, influenced by a recent model-specific technique for random forest interpretability. The proposed technique was evaluated through extensive experiments and shown to offer competitive interpretations compared to state-of-the-art techniques.
The Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog) is a neuropsychological tool that has been designed to assess the severity of cognitive symptoms of dementia. Personalized prediction of the changes in ADAS-Cog scores could help in timing therapeutic interventions in dementia and at-risk populations. In the present work, we compared single and multitask learning approaches to predict the changes in ADAS-Cog scores based on T1-weighted anatomical magnetic resonance imaging (MRI). In contrast to most machine learning-based prediction methods ADAS-Cog changes, we stratified the subjects based on their baseline diagnoses and evaluated the prediction performances in each group. Our experiments indicated a positive relationship between the predicted and observed ADAS-Cog score changes in each diagnostic group, suggesting that T1-weighted MRI has a predictive value for evaluating cognitive decline in the entire AD continuum. We further studied whether correction of the differences in the magnetic field strength of MRI would improve the ADAS-Cog score prediction. The partial least square-based domain adaptation slightly improved the prediction performance, but the improvement was marginal. In summary, this study demonstrated that ADAS-Cog change could be, to some extent, predicted based on anatomical MRI. Based on this study, the recommended method for learning the predictive models is a single-task regularized linear regression due to its simplicity and good performance. It appears important to combine the training data across all subject groups for the most effective predictive models.
The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to outliers. In contrast, l_p norms are known to be robust, but cannot be optimized via, e.g., stochastic gradient descent, as they are non-differentiable. We propose an algorithm inspired by so-called model-based optimization (MBO) [35, 36], which replaces a non-convex objective with a convex model function and alternates between optimizing the model function and updating the solution. We apply this to robust regression, proposing SADM, a stochastic variant of the Online Alternating Direction Method of Multipliers (OADM) [50] to solve the inner optimization in MBO. We show that SADM converges with the rate O(log T/T). Finally, we demonstrate experimentally (a) the robustness of l_p norms to outliers and (b) the efficiency of our proposed model-based algorithms in comparison with gradient methods on autoencoders and multi-target regression.
The adoption of machine learning in materials science has rapidly transformed materials property prediction. Hurdles limiting full capitalization of recent advancements in machine learning include the limited development of methods to learn the underlying interactions of multiple elements, as well as the relationships among multiple properties, to facilitate property prediction in new composition spaces. To address these issues, we introduce the Hierarchical Correlation Learning for Multi-property Prediction (H-CLMP) framework that seamlessly integrates (i) prediction using only a material's composition, (ii) learning and exploitation of correlations among target properties in multi-target regression, and (iii) leveraging training data from tangential domains via generative transfer learning. The model is demonstrated for prediction of spectral optical absorption of complex metal oxides spanning 69 3-cation metal oxide composition spaces. H-CLMP accurately predicts non-linear composition-property relationships in composition spaces for which no training data is available, which broadens the purview of machine learning to the discovery of materials with exceptional properties. This achievement results from the principled integration of latent embedding learning, property correlation learning, generative transfer learning, and attention models. The best performance is obtained using H-CLMP with Transfer learning (H-CLMP(T)) wherein a generative adversarial network is trained on computational density of states data and deployed in the target domain to augment prediction of optical absorption from composition. H-CLMP(T) aggregates multiple knowledge sources with a framework that is well-suited for multi-target regression across the physical sciences.
Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.
In this contribution, we predict the wellhead protection area (WHPA, target), the shape and extent of which is influenced by the distribution of hydraulic conductivity (K), from a small number of tracing experiments (predictor). Our first objective is to make stochastic predictions of the WHPA within the Bayesian Evidential Learning (BEL) framework, which aims to find a direct relationship between predictor and target using machine learning. This relationship is learned from a small set of training models (400) sampled from the prior distribution of K. The associated 400 pairs of simulated predictors and targets are obtained through forward modelling. Newly collected field data can then be directly used to predict the approximate posterior distribution of the corresponding WHPA. The uncertainty range of the posterior WHPA distribution is affected by the number and position of data sources (injection wells). Our second objective is to extend BEL to identify the optimal design of data source locations that minimizes the posterior uncertainty of the WHPA. This can be done explicitly, without averaging or approximating because once trained, the BEL model allows the computation of the posterior uncertainty corresponding to any new input data. We use the Modified Hausdorff Distance and the Structural Similarity index metrics to estimate the posterior uncertainty range of the WHPA. Increasing the number of injection wells effectively reduces the derived posterior WHPA uncertainty. Our approach can also estimate which injection wells are more informative than others, as validated through a k-fold cross-validation procedure. Overall, the application of BEL to experimental design makes it possible to identify the data sources maximizing the information content of any measurement data.
Multi-target prediction (MTP) serves as an umbrella term for machine learning tasks that concern the simultaneous prediction of multiple target variables. Classical instantiations are multi-label classification, multivariate regression, multi-task learning, dyadic prediction, zero-shot learning, network inference, and matrix completion. Despite the significant similarities, all these domains have evolved separately into distinct research areas over the last two decades. This led to the development of a plethora of highly-engineered methods, and created a substantially-high entrance barrier for machine learning practitioners that are not experts in the field. In this work we present a generic deep learning methodology that can be used for a wide range of multi-target prediction problems. We introduce a flexible multi-branch neural network architecture, partially configured via a questionnaire that helps end-users to select a suitable MTP problem setting for their needs. Experimental results for a wide range of domains illustrate that the proposed methodology manifests a competitive performance compared to methods from specific MTP domains.
There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated) multi-variate predictions. To do so, we propose to use copula functions applied to deep neural networks for inductive conformal prediction. We show that the proposed method ensures efficiency and validity for multi-target regression problems on various data sets.
The trend towards larger wind turbines and remote locations of wind farms fuels the demand for automated condition monitoring strategies that can reduce the operating cost and avoid unplanned downtime. Normal behaviour modelling has been introduced to detect anomalous deviations from normal operation based on the turbine's SCADA data. A growing number of machine learning models of the normal behaviour of turbine subsystems are being developed by wind farm managers to this end. However, these models need to be kept track of, be maintained and require frequent updates. This research explores multi-target models as a new approach to capturing a wind turbine's normal behaviour. We present an overview of multi-target regression methods, motivate their application and benefits in wind turbine condition monitoring, and assess their performance in a wind farm case study. We find that multi-target models are advantageous in comparison to single-target modelling in that they can reduce the cost and effort of practical condition monitoring without compromising on the accuracy. We also outline some areas of future research.
Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their optimal performance depends on massive amounts of training data and the tuning of an extended number of parameters. As a countermeasure, some deep-forest methods have been recently proposed, as efficient and low-scale solutions. Despite that, these approaches simply employ label classification probabilities as induced features and primarily focus on traditional classification and regression tasks, leaving multi-output prediction under-explored. Moreover, recent work has demonstrated that tree-embeddings are highly representative, especially in structured output prediction. In this direction, we propose a novel deep tree-ensemble (DTE) model, where every layer enriches the original feature set with a representation learning component based on tree-embeddings. In this paper, we specifically focus on two structured output prediction tasks, namely multi-label classification and multi-target regression. We conducted experiments using multiple benchmark datasets and the obtained results confirm that our method provides superior results to state-of-the-art methods in both tasks.
A key problem in computational sustainability is to understand the distribution of species across landscapes over time. This question gives rise to challenging large-scale prediction problems since (i) hundreds of species have to be simultaneously modeled and (ii) the survey data are usually inflated with zeros due to the absence of species for a large number of sites. The problem of tackling both issues simultaneously, which we refer to as the zero-inflated multi-target regression problem, has not been addressed by previous methods in statistics and machine learning. In this paper, we propose a novel deep model for the zero-inflated multi-target regression problem. To this end, we first model the joint distribution of multiple response variables as a multivariate probit model and then couple the positive outcomes with a multivariate log-normal distribution. By penalizing the difference between the two distributions' covariance matrices, a link between both distributions is established. The whole model is cast as an end-to-end learning framework and we provide an efficient learning algorithm for our model that can be fully implemented on GPUs. We show that our model outperforms the existing state-of-the-art baselines on two challenging real-world species distribution datasets concerning bird and fish populations.
In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.
Multi-objective optimization (MOO) problems are prevalent in machine learning. These problems have a set of optimal solutions, called the Pareto front, where each point on the front represents a different trade-off between possibly conflicting objectives. Recent MOO methods can target a specific desired ray in loss space however, most approaches still face two grave limitations: (i) A separate model has to be trained for each point on the front; and (ii) The exact trade-off must be known before the optimization process. Here, we tackle the problem of learning the entire Pareto front, with the capability of selecting a desired operating point on the front after training. We call this new setup Pareto-Front Learning (PFL). We describe an approach to PFL implemented using HyperNetworks, which we term Pareto HyperNetworks (PHNs). PHN learns the entire Pareto front simultaneously using a single hypernetwork, which receives as input a desired preference vector and returns a Pareto-optimal model whose loss vector is in the desired ray. The unified model is runtime efficient compared to training multiple models and generalizes to new operating points not used during training. We evaluate our method on a wide set of problems, from multi-task regression and classification to fairness. PHNs learn the entire Pareto front at roughly the same time as learning a single point on the front and at the same time reach a better solution set. Furthermore, we show that PHNs can scale to generate large models like ResNet18. PFL opens the door to new applications where models are selected based on preferences that are only available at run time.
Intentional manipulation of invoices that lead to undervaluation of trade goods is the most common type of customs fraud to avoid ad valorem duties and taxes. To secure government revenue without interrupting legitimate trade flows, customs administrations around the world strive to develop ways to detect illicit trades. This paper proposes DATE, a model of Dual-task Attentive Tree-aware Embedding, to classify and rank illegal trade flows that contribute the most to the overall customs revenue when caught. The strength of DATE comes from combining a tree-based model for interpretability and transaction-level embeddings with dual attention mechanisms. To accurately identify illicit transactions and predict tax revenue, DATE learns simultaneously from illicitness and surtax of each transaction. With a five-year amount of customs import data with a test illicit ratio of 2.24%, DATE shows a remarkable precision of 92.7% on illegal cases and a recall of 49.3% on revenue after inspecting only 1% of all trade flows. We also discuss issues on deploying DATE in Nigeria Customs Service, in collaboration with the World Customs Organization.
The data made available for analysis are becoming more and more complex along several directions: high dimensionality, number of examples and the amount of labels per example. This poses a variety of challenges for the existing machine learning methods: coping with dataset with a large number of examples that are described in a high-dimensional space and not all examples have labels provided. For example, when investigating the toxicity of chemical compounds there are a lot of compounds available, that can be described with information rich high-dimensional representations, but not all of the compounds have information on their toxicity. To address these challenges, we propose semi-supervised learning of feature ranking. The feature rankings are learned in the context of classification and regression as well as in the context of structured output prediction (multi-label classification, hierarchical multi-label classification and multi-target regression). To the best of our knowledge, this is the first work that treats the task of feature ranking within the semi-supervised structured output prediction context. More specifically, we propose two approaches that are based on tree ensembles and the Relief family of algorithms. The extensive evaluation across 38 benchmark datasets reveals the following: Random Forests perform the best for the classification-like tasks, while for the regression-like tasks Extra-PCTs perform the best, Random Forests are the most efficient method considering induction times across all tasks, and semi-supervised feature rankings outperform their supervised counterpart across a majority of the datasets from the different tasks.
The task of redescription mining explores ways to re-describe different subsets of entities contained in a dataset and to reveal non-trivial associations between different subsets of attributes, called views. This interesting and challenging task is encountered in different scientific fields, and is addressed by a number of approaches that obtain redescriptions and allow for the exploration and analyses of attribute associations. The main limitation of existing approaches to this task is their inability to use more than two views. Our work alleviates this drawback. We present a memory efficient, extensible multi-view redescription mining framework that can be used to relate multiple, i.e. more than two views, disjoint sets of attributes describing one set of entities. The framework can use any multi-target regression or multi-label classification algorithm, with models that can be represented as sets of rules, to generate redescriptions. Multi-view redescriptions are built using incremental view-extending heuristic from initially created two-view redescriptions. In this work, we use different types of Predictive Clustering trees algorithms (regular, extra, with random output selection) and the Random Forest thereof in order to improve the quality of final redescription sets and/or execution time needed to generate them. We provide multiple performance analyses of the proposed framework and compare it against the naive approach to multi-view redescription mining. We demonstrate the usefulness of the proposed multi-view extension on several datasets, including a use-case on understanding of machine learning models - a topic of growing importance in machine learning and artificial intelligence in general.