We provide an analytical characterization of the model flexibility of the synthetic control method (SCM) in the familiar form of degrees of freedom. We obtain estimable information criteria. These may be used to circumvent cross-validation when selecting either the weighting matrix in the SCM with covariates, or the tuning parameter in model averaging or penalized variants of SCM. We assess the impact of car license rationing in Tianjin and make a novel use of SCM; while a natural match is available, it and other donors are noisy, inviting the use of SCM to average over approximately matching donors. The very large number of candidate donors calls for model averaging or penalized variants of SCM and, with short pre-treatment series, model selection per information criteria outperforms that per cross-validation.
Machine learning (ML) models are typically optimized for their accuracy on a given dataset. However, this predictive criterion rarely captures all desirable properties of a model, in particular how well it matches a domain expert's understanding of a task. Underspecification refers to the existence of multiple models that are indistinguishable in their in-domain accuracy, even though they differ in other desirable properties such as out-of-distribution (OOD) performance. Identifying these situations is critical for assessing the reliability of ML models. We formalize the concept of underspecification and propose a method to identify and partially address it. We train multiple models with an independence constraint that forces them to implement different functions. They discover predictive features that are otherwise ignored by standard empirical risk minimization (ERM), which we then distill into a global model with superior OOD performance. Importantly, we constrain the models to align with the data manifold to ensure that they discover meaningful features. We demonstrate the method on multiple datasets in computer vision (collages, WILDS-Camelyon17, GQA) and discuss general implications of underspecification. Most notably, in-domain performance cannot serve for OOD model selection without additional assumptions.
The expressive and computationally inexpensive bipartite Graph Neural Networks (GNN) have been shown to be an important component of deep learning based Mixed-Integer Linear Program (MILP) solvers. Recent works have demonstrated the effectiveness of such GNNs in replacing the branching (variable selection) heuristic in branch-and-bound (B&B) solvers. These GNNs are trained, offline and on a collection of MILPs, to imitate a very good but computationally expensive branching heuristic, strong branching. Given that B&B results in a tree of sub-MILPs, we ask (a) whether there are strong dependencies exhibited by the target heuristic among the neighboring nodes of the B&B tree, and (b) if so, whether we can incorporate them in our training procedure. Specifically, we find that with the strong branching heuristic, a child node's best choice was often the parent's second-best choice. We call this the "lookback" phenomenon. Surprisingly, the typical branching GNN of Gasse et al. (2019) often misses this simple "answer". To imitate the target behavior more closely by incorporating the lookback phenomenon in GNNs, we propose two methods: (a) target smoothing for the standard cross-entropy loss function, and (b) adding a Parent-as-Target (PAT) Lookback regularizer term. Finally, we propose a model selection framework to incorporate harder-to-formulate objectives such as solving time in the final models. Through extensive experimentation on standard benchmark instances, we show that our proposal results in up to 22% decrease in the size of the B&B tree and up to 15% improvement in the solving times.
We study the problem of model selection in bandit scenarios in the presence of nested policy classes, with the goal of obtaining simultaneous adversarial and stochastic ("best of both worlds") high-probability regret guarantees. Our approach requires that each base learner comes with a candidate regret bound that may or may not hold, while our meta algorithm plays each base learner according to a schedule that keeps the base learner's candidate regret bounds balanced until they are detected to violate their guarantees. We develop careful mis-specification tests specifically designed to blend the above model selection criterion with the ability to leverage the (potentially benign) nature of the environment. We recover the model selection guarantees of the CORRAL algorithm for adversarial environments, but with the additional benefit of achieving high probability regret bounds, specifically in the case of nested adversarial linear bandits. More importantly, our model selection results also hold simultaneously in stochastic environments under gap assumptions. These are the first theoretical results that achieve best of both world (stochastic and adversarial) guarantees while performing model selection in (linear) bandit scenarios.
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a perpendicular formulation to conventional model building, we start from the linear system of phenomenological constraints and asymptotically derive the distribution over all viable distributions that satisfy the provided set of constraints. The MaxEnt distribution plays a special role, as it is the most typical among all phenomenologically viable distributions representing a good expansion point for large-N techniques. This enables us to consistently formulate hypothesis testing in a fully-data driven manner. The appropriate parametric model which is supported by the data can be always deduced at the end of model selection. In the MaxEnt framework, we recover major scores and selection procedures used in multiple applications and assess their ability to capture associations in the data-generating process and identify the most generalizable model. This data-driven counterpart of standard model selection demonstrates the unifying prospective of the deductive logic advocated by MaxEnt principle, while potentially shedding new insights to the inverse problem.
Early diagnosis of Alzheimer's disease (AD) is crucial in facilitating preventive care and delay progression. Speech based automatic AD screening systems provide a non-intrusive and more scalable alternative to other clinical screening techniques. Scarcity of such specialist data leads to uncertainty in both model selection and feature learning when developing such systems. To this end, this paper investigates the use of feature and model combination approaches to improve the robustness of domain fine-tuning of BERT and Roberta pre-trained text encoders on limited data, before the resulting embedding features being fed into an ensemble of backend classifiers to produce the final AD detection decision via majority voting. Experiments conducted on the ADReSS20 Challenge dataset suggest consistent performance improvements were obtained using model and feature combination in system development. State-of-the-art AD detection accuracies of 91.67 percent and 93.75 percent were obtained using manual and ASR speech transcripts respectively on the ADReSS20 test set consisting of 48 elderly speakers.
Recently, Miller et al. showed that a model's in-distribution (ID) accuracy has a strong linear correlation with its out-of-distribution (OOD) accuracy on several OOD benchmarks -- a phenomenon they dubbed ''accuracy-on-the-line''. While a useful tool for model selection (i.e., the model most likely to perform the best OOD is the one with highest ID accuracy), this fact does not help estimate the actual OOD performance of models without access to a labeled OOD validation set. In this paper, we show a similar but surprising phenomenon also holds for the agreement between pairs of neural network classifiers: whenever accuracy-on-the-line holds, we observe that the OOD agreement between the predictions of any two pairs of neural networks (with potentially different architectures) also observes a strong linear correlation with their ID agreement. Furthermore, we observe that the slope and bias of OOD vs ID agreement closely matches that of OOD vs ID accuracy. This phenomenon, which we call agreement-on-the-line, has important practical applications: without any labeled data, we can predict the OOD accuracy of classifiers}, since OOD agreement can be estimated with just unlabeled data. Our prediction algorithm outperforms previous methods both in shifts where agreement-on-the-line holds and, surprisingly, when accuracy is not on the line. This phenomenon also provides new insights into deep neural networks: unlike accuracy-on-the-line, agreement-on-the-line appears to only hold for neural network classifiers.
The well-developed ETS (ExponenTial Smoothing or Error, Trend, Seasonality) method incorporating a family of exponential smoothing models in state space representation has been widely used for automatic forecasting. The existing ETS method uses information criteria for model selection by choosing an optimal model with the smallest information criterion among all models fitted to a given time series. The ETS method under such a model selection scheme suffers from computational complexity when applied to large-scale time series data. To tackle this issue, we propose an efficient approach for ETS model selection by training classifiers on simulated data to predict appropriate model component forms for a given time series. We provide a simulation study to show the model selection ability of the proposed approach on simulated data. We evaluate our approach on the widely used forecasting competition data set M4, in terms of both point forecasts and prediction intervals. To demonstrate the practical value of our method, we showcase the performance improvements from our approach on a monthly hospital data set.
The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.
Assessment of model fitness is a key part of machine learning. The standard paradigm is to learn models by minimizing a chosen loss function averaged over training data, with the aim of achieving small losses on future data. In this paper, we consider the use of a finite calibration data set to characterize the future, out-of-sample losses of a model. We propose a simple model diagnostic tool that provides finite-sample guarantees under weak assumptions. The tool is simple to compute and to interpret. Several numerical experiments are presented to show how the proposed method quantifies the impact of distribution shifts, aids the analysis of regression, and enables model selection as well as hyper-parameter tuning.
End-to-end AutoML has attracted intensive interests from both academia and industry which automatically searches for ML pipelines in a space induced by feature engineering, algorithm/model selection, and hyper-parameter tuning. Existing AutoML systems, however, suffer from scalability issues when applying to application domains with large, high-dimensional search spaces. We present VolcanoML, a scalable and extensible framework that facilitates systematic exploration of large AutoML search spaces. VolcanoML introduces and implements basic building blocks that decompose a large search space into smaller ones, and allows users to utilize these building blocks to compose an execution plan for the AutoML problem at hand. VolcanoML further supports a Volcano-style execution model -- akin to the one supported by modern database systems -- to execute the plan constructed. Our evaluation demonstrates that, not only does VolcanoML raise the level of expressiveness for search space decomposition in AutoML, it also leads to actual findings of decomposition strategies that are significantly more efficient than the ones employed by state-of-the-art AutoML systems such as auto-sklearn. This paper is the extended version of the initial VolcanoML paper appeared in VLDB 2021.
Given a graph learning task, such as link prediction, on a new graph, how can we select the best method as well as its hyperparameters (collectively called a model) without having to train or evaluate any model on the new graph? Model selection for graph learning has been largely ad hoc. A typical approach has been to apply popular methods to new datasets, but this is often suboptimal. On the other hand, systematically comparing models on the new graph quickly becomes too costly, or even impractical. In this work, we develop the first meta-learning approach for evaluation-free graph learning model selection, called MetaGL, which utilizes the prior performances of existing methods on various benchmark graph datasets to automatically select an effective model for the new graph, without any model training or evaluations. To quantify similarities across a wide variety of graphs, we introduce specialized meta-graph features that capture the structural characteristics of a graph. Then we design G-M network, which represents the relations among graphs and models, and develop a graph-based meta-learner operating on this G-M network, which estimates the relevance of each model to different graphs. Extensive experiments show that using MetaGL to select a model for the new graph greatly outperforms several existing meta-learning techniques tailored for graph learning model selection (up to 47% better), while being extremely fast at test time (~1 sec).
As restricted quantum computers are slowly becoming a reality, the search for meaningful first applications intensifies. In this domain, one of the more investigated approaches is the use of a special type of quantum circuit - a so-called quantum neural network -- to serve as a basis for a machine learning model. Roughly speaking, as the name suggests, a quantum neural network can play a similar role to a neural network. However, specifically for applications in machine learning contexts, very little is known about suitable circuit architectures, or model hyperparameters one should use to achieve good learning performance. In this work, we apply the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most influential for their predictive performance. We analyze one of the most typically used quantum neural network architectures. We then apply this to $7$ open-source datasets from the OpenML-CC18 classification benchmark whose number of features is small enough to fit on quantum hardware with less than $20$ qubits. Three main levels of importance were detected from the ranking of hyperparameters obtained with functional ANOVA. Our experiment both confirmed expected patterns and revealed new insights. For instance, setting well the learning rate is deemed the most critical hyperparameter in terms of marginal contribution on all datasets, whereas the particular choice of entangling gates used is considered the least important except on one dataset. This work introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.
Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC) and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this paper, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample size and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC.
The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.
Systems driven by Brownian motion are ubiquitous. A prevailing challenge is inferring, from data, the diffusion and kinetic parameters that describe these stochastic processes. In this work, we investigate a multi-state diffusion process that arises in the context of single particle tracking (SPT), wherein the motion of a particle is governed by a discrete set of diffusive states, and the tendency of the particle to switch between these states is modeled as a random process. We consider two models for this behavior: a mixture model and a hidden Markov model (HMM). For both, we adopt a Bayesian approach to sample the distributions of the underlying parameters and implement a Markov Chain Monte Carlo (MCMC) scheme to compute the posterior distributions, as in Das, Cairo, Coombs (2009). The primary contribution of this work is a study of the robustness of this method to infer parameters of a three-state HMM, and a discussion of the challenges and degeneracies that arise from considering three states. Finally, we investigate the problem of determining the number of diffusive states using model selection criteria. We present results from simulated data that demonstrate proof of concept, as well as apply our method to experimentally measured single molecule diffusion trajectories of monomeric phosphoinositide-dependent kinase-1 (PDK1) on a synthetic target membrane where it can associate with its binding partner protein kinase C alpha isoform (PKC$\alpha$) to form a heterodimer detected by its significantly lower diffusivity. All matlab software is available here: \url{https://github.com/MathBioCU/SingleMolecule}
Consider the problem of imputing missing values in a dataset. One the one hand, conventional approaches using iterative imputation benefit from the simplicity and customizability of learning conditional distributions directly, but suffer from the practical requirement for appropriate model specification of each and every variable. On the other hand, recent methods using deep generative modeling benefit from the capacity and efficiency of learning with neural network function approximators, but are often difficult to optimize and rely on stronger data assumptions. In this work, we study an approach that marries the advantages of both: We propose *HyperImpute*, a generalized iterative imputation framework for adaptively and automatically configuring column-wise models and their hyperparameters. Practically, we provide a concrete implementation with out-of-the-box learners, optimizers, simulators, and extensible interfaces. Empirically, we investigate this framework via comprehensive experiments and sensitivities on a variety of public datasets, and demonstrate its ability to generate accurate imputations relative to a strong suite of benchmarks. Contrary to recent work, we believe our findings constitute a strong defense of the iterative imputation paradigm.
Outlier detection (OD) literature exhibits numerous algorithms as it applies to diverse domains. However, given a new detection task, it is unclear how to choose an algorithm to use, nor how to set its hyperparameter(s) (HPs) in unsupervised settings. HP tuning is an ever-growing problem with the arrival of many new detectors based on deep learning, which usually come with a long list of HPs. Surprisingly, the issue of model selection in the outlier mining literature has been "the elephant in the room"; a significant factor in unlocking the utmost potential of deep methods, yet little said or done to systematically tackle the issue. In the first part of this paper, we conduct the first large-scale analysis on the HP sensitivity of deep OD methods, and through more than 35,000 trained models, quantitatively demonstrate that model selection is inevitable. Next, we design a HP-robust and scalable deep hyper-ensemble model called ROBOD that assembles models with varying HP configurations, bypassing the choice paralysis. Importantly, we introduce novel strategies to speed up ensemble training, such as parameter sharing, batch/simultaneous training, and data subsampling, that allow us to train fewer models with fewer parameters. Extensive experiments on both image and tabular datasets show that ROBOD achieves and retains robust, state-of-the-art detection performance as compared to its modern counterparts, while taking only $2$-$10$\% of the time by the naive hyper-ensemble with independent training.
For 3D medical image (e.g. CT and MRI) segmentation, the difficulty of segmenting each slice in a clinical case varies greatly. Previous research on volumetric medical image segmentation in a slice-by-slice manner conventionally use the identical 2D deep neural network to segment all the slices of the same case, ignoring the data heterogeneity among image slices. In this paper, we focus on multi-modal 3D MRI brain tumor segmentation and propose a dynamic architecture network named Med-DANet based on adaptive model selection to achieve effective accuracy and efficiency trade-off. For each slice of the input 3D MRI volume, our proposed method learns a slice-specific decision by the Decision Network to dynamically select a suitable model from the predefined Model Bank for the subsequent 2D segmentation task. Extensive experimental results on both BraTS 2019 and 2020 datasets show that our proposed method achieves comparable or better results than previous state-of-the-art methods for 3D MRI brain tumor segmentation with much less model complexity. Compared with the state-of-the-art 3D method TransBTS, the proposed framework improves the model efficiency by up to 3.5x without sacrificing the accuracy. Our code will be publicly available soon.