The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is often the case when working with real data. This paper focuses on purely machine learned and purely knowledge-based BNs and investigates their differences in terms of graphical structure and how well the implied statistical models explain the data. The tests are based on four previous case studies whose BN structure was determined by domain knowledge. Using various metrics, we compare the knowledge-based graphs to the machine learned graphs generated from various algorithms implemented in TETRAD spanning all three classes of learning. The results show that, while the algorithms produce graphs with much higher model selection score, the knowledge-based graphs are more accurate predictors of variables of interest. Maximising score fitting is ineffective in the presence of limited sample size because the fitting becomes increasingly distorted with limited data, guiding algorithms towards graphical patterns that share higher fitting scores and yet deviate considerably from the true graph. This highlights the value of causal knowledge in these cases, as well as the need for more appropriate fitting scores suitable for limited data. Lastly, the experiments also provide new evidence that support the notion that results from simulated data tell us little about actual real-world performance.
Many online applications running on live traffic are powered by machine learning models, for which training, validation, and hyper-parameter tuning are conducted on historical data. However, it is common for models demonstrating strong performance in offline analysis to yield poorer performance when deployed online. This problem is a consequence of the difficulty of training on historical data in non-stationary environments. Moreover, the machine learning metrics used for model selection may not sufficiently correlate with real-world business metrics used to determine the success of the applications being tested. These problems are particularly prominent in the Real-Time Bidding (RTB) domain, in which ML models power bidding strategies, and a change in models will likely affect performance of the advertising campaigns. In this work, we present Automatic Model Selector (AMS), a system for scalable online selection of RTB bidding strategies based on real-world performance metrics. AMS employs Multi-Armed Bandits (MAB) to near-simultaneously run and evaluate multiple models against live traffic, allocating the most traffic to the best-performing models while decreasing traffic to those with poorer online performance, thereby minimizing the impact of inferior models on overall campaign performance. The reliance on offline data is avoided, instead making model selections on a case-by-case basis according to actionable business goals. AMS allows new models to be safely introduced into live campaigns as soon as they are developed, minimizing the risk to overall performance. In live-traffic tests on multiple ad campaigns, the AMS system proved highly effective at improving ad campaign performance.
We address the task of domain generalization, where the goal is to train a predictive model such that it is able to generalize to a new, previously unseen domain. We choose a hierarchical generative approach within the framework of variational autoencoders and propose a domain-unsupervised algorithm that is able to generalize to new domains without domain supervision. We show that our method is able to learn representations that disentangle domain-specific information from class-label specific information even in complex settings where domain structure is not observed during training. Our interpretable method outperforms previously proposed generative algorithms for domain generalization as well as other non-generative state-of-the-art approaches in several hierarchical domain settings including sequential overlapped near continuous domain shift. It also achieves competitive performance on the standard domain generalization benchmark dataset PACS compared to state-of-the-art approaches which rely on observing domain-specific information during training, as well as another domain unsupervised method. Additionally, we proposed model selection purely based on Evidence Lower Bound (ELBO) and also proposed weak domain supervision where implicit domain information can be added into the algorithm.
Semantic segmentation aims to robustly predict coherent class labels for entire regions of an image. It is a scene understanding task that powers real-world applications (e.g., autonomous navigation). One important application, the use of imagery for automated semantic understanding of pedestrian environments, provides remote mapping of accessibility features in street environments. This application (and others like it) require detailed geometric information of geographical objects. Semantic segmentation is a prerequisite for this task since it maps contiguous regions of the same class as single entities. Importantly, semantic segmentation uses like ours are not pixel-wise outcomes; however, most of their quantitative evaluation metrics (e.g., mean Intersection Over Union) are based on pixel-wise similarities to a ground-truth, which fails to emphasize over- and under-segmentation properties of a segmentation model. Here, we introduce a new metric to assess region-based over- and under-segmentation. We analyze and compare it to other metrics, demonstrating that the use of our metric lends greater explainability to semantic segmentation model performance in real-world applications.
Selecting a small set of informative features from a large number of possibly noisy candidates is a challenging problem with many applications in machine learning and approximate Bayesian computation. In practice, the cost of computing informative features also needs to be considered. This is particularly important for networks because the computational costs of individual features can span several orders of magnitude. We addressed this issue for the network model selection problem using two approaches. First, we adapted nine feature selection methods to account for the cost of features. We show for two classes of network models that the cost can be reduced by two orders of magnitude without considerably affecting classification accuracy (proportion of correctly identified models). Second, we selected features using pilot simulations with smaller networks. This approach reduced the computational cost by a factor of 50 without affecting classification accuracy. To demonstrate the utility of our approach, we applied it to three different yeast protein interaction networks and identified the best-fitting duplication divergence model.
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to de-trend a time series or normalize a spectrum. In these contexts, investigators often choose a polynomial basis, or a Fourier basis, or wavelets, or something equally general. They also choose an order, or number of basis functions to fit, and (often) some kind of regularization. We discuss how this basis-function fitting is done, with ordinary least squares and extensions thereof. We emphasize that it is often valuable to choose far more parameters than data points, despite folk rules to the contrary: Suitably regularized models with enormous numbers of parameters generalize well and make good predictions for held-out data; over-fitting is not (mainly) a problem of having too many parameters. It is even possible to take the limit of infinite parameters, at which, if the basis and regularization are chosen correctly, the least-squares fit becomes the mean of a Gaussian process. We recommend cross-validation as a good empirical method for model selection (for example, setting the number of parameters and the form of the regularization), and jackknife resampling as a good empirical method for estimating the uncertainties of the predictions made by the model. We also give advice for building stable computational implementations.
Hyperkalemia is a potentially life-threatening condition that can lead to fatal arrhythmias. Early identification of high risk patients can inform clinical care to mitigate the risk. While hyperkalemia is often a complication of acute kidney injury (AKI), it also occurs in the absence of AKI. We developed predictive models to identify intensive care unit (ICU) patients at risk of developing hyperkalemia by using the Medical Information Mart for Intensive Care (MIMIC) and the eICU Collaborative Research Database (eICU-CRD). Our methodology focused on building multiple models, optimizing for interpretability through model selection, and simulating various clinical scenarios. In order to determine if our models perform accurately on patients with and without AKI, we evaluated the following clinical cases: (i) predicting hyperkalemia after AKI within 14 days of ICU admission, (ii) predicting hyperkalemia within 14 days of ICU admission regardless of AKI status, and compared different lead times for (i) and (ii). Both clinical scenarios were modeled using logistic regression (LR), random forest (RF), and XGBoost. Using observations from the first day in the ICU, our models were able to predict hyperkalemia with an AUC of (i) 0.79, 0.81, 0.81 and (ii) 0.81, 0.85, 0.85 for LR, RF, and XGBoost respectively. We found that 4 out of the top 5 features were consistent across the models. AKI stage was significant in the models that included all patients with or without AKI, but not in the models which only included patients with AKI. This suggests that while AKI is important for hyperkalemia, the specific stage of AKI may not be as important. Our findings require further investigation and confirmation.
This paper aims to study data driven model selection criteria for a large class of time series, which includes ARMA or AR($\infty$) processes, as well as GARCH or ARCH($\infty$), APARCH and many others processes. We tackled the challenging issue of designing adaptive criteria which enjoys the strong consistency property. When the observations are generated from one of the aforementioned models, the new criteria, select the true model almost surely asymptotically. The proposed criteria are based on the minimization of a penalized contrast akin to the Hannan and Quinn's criterion and then involved a term which is known for most classical time series models and for more complex models, this term can be data driven calibrated. Monte-Carlo experiments and an illustrative example on the CAC 40 index are performed to highlight the obtained results.
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Uniqueness conditions and fitting methods have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms, $R$, and their individual ranks, $L_r$, has only recently started to attract significant attention, mainly through regularization-based approaches which entail the need to tune the regularization parameter(s). In this work, we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level \emph{hierarchical} probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is \emph{jointly} imposed. Ranks are then estimated from the numbers of blocks ($R$) and columns ($L_r$) of non-negligible energy. Approximate posterior inference is implemented, within the variational inference framework. The resulting iterative algorithm completely avoids hyperparameter tuning, which is a significant defect of regularization-based methods. Alternative probabilistic models are also explored and the connections with their regularization-based counterparts are brought to light with the aid of the associated maximum a-posteriori (MAP) estimators. We report simulation results with both synthetic and real-word data, which demonstrate the merits of the proposed method in terms of both rank estimation and model fitting as compared to state-of-the-art relevant methods.
Dynamic early exiting aims to accelerate the inference of pre-trained language models (PLMs) by emitting predictions in internal layers without passing through the entire model. In this paper, we empirically analyze the working mechanism of dynamic early exiting and find that it faces a performance bottleneck under high speed-up ratios. On one hand, the PLMs' representations in shallow layers lack high-level semantic information and thus are not sufficient for accurate predictions. On the other hand, the exiting decisions made by internal classifiers are unreliable, leading to wrongly emitted early predictions. We instead propose a new framework for accelerating the inference of PLMs, CascadeBERT, which dynamically selects proper-sized and complete models in a cascading manner, providing comprehensive representations for predictions. We further devise a difficulty-aware objective, encouraging the model to output the class probability that reflects the real difficulty of each instance for a more reliable cascading mechanism. Experimental results show that CascadeBERT can achieve an overall 15\% improvement under 4$\times$ speed-up compared with existing dynamic early exiting methods on six classification tasks, yielding more calibrated and accurate predictions.
Machine Learning applications have brought new insights into a secondary analysis of medical data. Machine Learning helps to develop new drugs, define populations susceptible to certain illnesses, identify predictors of many common diseases. At the same time, Machine Learning results depend on convolution of many factors, including feature selection, class (im)balance, algorithm preference, and performance metrics. In this paper, we present explainable multi-class classification of a large medical data set. We in details discuss knowledge-based feature engineering, data set balancing, best model selection, and parameter tuning. Six algorithms are used in this study: Support Vector Machine (SVM), Na\"ive Bayes, Gradient Boosting, Decision Trees, Random Forest, and Logistic Regression. Our empirical evaluation is done on the UCI Diabetes 130-US hospitals for years 1999-2008 dataset, with the task to classify patient hospital re-admission stay into three classes: 0 days, <30 days, or > 30 days. Our results show that using 23 medication features in learning experiments improves Recall of five out of the six applied learning algorithms. This is a new result that expands the previous studies conducted on the same data. Gradient Boosting and Random Forest outperformed other algorithms in terms of the three-class classification Accuracy.
Machine learning techniques have been developed to learn from complete data. When missing values exist in a dataset, the incomplete data should be preprocessed separately by removing data points with missing values or imputation. In this paper, we propose an online approach to handle missing values while a classification model is learnt. To reach this goal, we develop a multi-objective optimization model with two objective functions for imputation and model selection. We also propose three formulations for imputation objective function. We use an evolutionary algorithm based on NSGA II to find the optimal solutions as the Pareto solutions. We investigate the reliability and robustness of the proposed model using experiments by defining several scenarios in dealing with missing values and classification. We also describe how the proposed model can contribute to medical informatics. We compare the performance of three different formulations via experimental results. The proposed model results get validated by comparing with a comparable literature.
We provide a simple method to combine stochastic bandit algorithms. Our approach is based on a "meta-UCB" procedure that treats each of $N$ individual bandit algorithms as arms in a higher-level $N$-armed bandit problem that we solve with a variant of the classic UCB algorithm. Our final regret depends only on the regret of the base algorithm with the best regret in hindsight. This approach provides an easy and intuitive alternative strategy to the CORRAL algorithm for adversarial bandits, without requiring the stability conditions imposed by CORRAL on the base algorithms. Our results match lower bounds in several settings, and we provide empirical validation of our algorithm on misspecified linear bandit and model selection problems.
We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base algorithm comes with a candidate regret bound that may or may not hold during all rounds. In each round, our approach plays a base algorithm to keep the candidate regret bounds of all remaining base algorithms balanced, and eliminates algorithms that violate their candidate bound. We prove that the total regret of this approach is bounded by the best valid candidate regret bound times a multiplicative factor. This factor is reasonably small in several applications, including linear bandits and MDPs with nested function classes, linear bandits with unknown misspecification, and LinUCB applied to linear bandits with different confidence parameters. We further show that, under a suitable gap-assumption, this factor only scales with the number of base algorithms and not their complexity when the number of rounds is large enough. Finally, unlike recent efforts in model selection for linear stochastic bandits, our approach is versatile enough to also cover cases where the context information is generated by an adversarial environment, rather than a stochastic one.
As the main workhorse for model selection, Cross Validation (CV) has achieved an empirical success due to its simplicity and intuitiveness. However, despite its ubiquitous role, CV often falls into the following notorious dilemmas. On the one hand, for small data cases, CV suffers a conservatively biased estimation, since some part of the limited data has to hold out for validation. On the other hand, for large data cases, CV tends to be extremely cumbersome, e.g., intolerant time-consuming, due to the repeated training procedures. Naturally, a straightforward ambition for CV is to validate the models with far less computational cost, while making full use of the entire given data-set for training. Thus, instead of holding out the given data, a cheap and theoretically guaranteed auxiliary/augmented validation is derived strategically in this paper. Such an embarrassingly simple strategy only needs to train models on the entire given data-set once, making the model-selection considerably efficient. In addition, the proposed validation approach is suitable for a wide range of learning settings due to the independence of both augmentation and out-of-sample estimation on learning process. In the end, we demonstrate the accuracy and computational benefits of our proposed method by extensive evaluation on multiple data-sets, models and tasks.
A central issue of many statistical learning problems is to select an appropriate model from a set of candidate models. Large models tend to inflate the variance (or overfitting), while small models tend to cause biases (or underfitting) for a given fixed dataset. In this work, we address the critical challenge of model selection to strike a balance between model fitting and model complexity, thus gaining reliable predictive power. We consider the task of approaching the theoretical limit of statistical learning, meaning that the selected model has the predictive performance that is as good as the best possible model given a class of potentially misspecified candidate models. We propose a generalized notion of Takeuchi's information criterion and prove that the proposed method can asymptotically achieve the optimal out-sample prediction loss under reasonable assumptions. It is the first proof of the asymptotic property of Takeuchi's information criterion to our best knowledge. Our proof applies to a wide variety of nonlinear models, loss functions, and high dimensionality (in the sense that the models' complexity can grow with sample size). The proposed method can be used as a computationally efficient surrogate for leave-one-out cross-validation. Moreover, for modeling streaming data, we propose an online algorithm that sequentially expands the model complexity to enhance selection stability and reduce computation cost. Experimental studies show that the proposed method has desirable predictive power and significantly less computational cost than some popular methods.
Non-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable for non-parametric statistical modelling with automatic model selection. We demonstrate PrAda-net on simulated data, where wecompare the test error performance, variable importance and variable subset identification properties of PrAda-net to other lasso-based regularization approaches for neural networks. We also apply PrAda-net to the massive U.K. black smoke data set, to demonstrate how PrAda-net can be used to model complex and heterogeneous data with spatial and temporal components. In contrast to classical, statistical non-parametric approaches, PrAda-net requires no preliminary modeling to select the functional forms of the additive components, yet still results in an interpretable model representation.
Recent research on speech enhancement (SE) has seen the emergence of deep-learning-based methods. It is still a challenging task to determine the effective ways to increase the generalizability of SE under diverse test conditions. In this study, we combine zero-shot learning and ensemble learning to propose a zero-shot model selection (ZMOS) approach to increase the generalization of SE performance. The proposed approach is realized in the offline and online phases. The offline phase clusters the entire set of training data into multiple subsets and trains a specialized SE model (termed component SE model) with each subset. The online phase selects the most suitable component SE model to perform the enhancement. Furthermore, two selection strategies were developed: selection based on the quality score (QS) and selection based on the quality embedding (QE). Both QS and QE were obtained using a Quality-Net, a non-intrusive quality assessment network. Experimental results confirmed that the proposed ZMOS approach can achieve better performance in both seen and unseen noise types compared to the baseline systems and other model selection systems, which indicates the effectiveness of the proposed approach in providing robust SE performance.
The effective application of representation learning to real-world problems requires both techniques for learning useful representations, and also robust ways to evaluate properties of representations. Recent work in disentangled representation learning has shown that unsupervised representation learning approaches rely on fully supervised disentanglement metrics, which assume access to labels for ground-truth factors of variation. In many real-world cases ground-truth factors are expensive to collect, or difficult to model, such as for perception. Here we empirically show that a weakly-supervised downstream task based on odd-one-out observations is suitable for model selection by observing high correlation on a difficult downstream abstract visual reasoning task. We also show that a bespoke metric-learning VAE model which performs highly on this task also out-performs other standard unsupervised and a weakly-supervised disentanglement model across several metrics.
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the $\ell_1$-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the $\ell_1$-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the $\ell_1$-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach.