In this paper, we are concerned with image classification with deep convolutional neural networks (CNNs). We focus on the following question: given a set of candidate CNN models, how to select the right one with the best generalization property for the current task? Current model selection methods all require access to a batch of labeled data for computing a pre-specified performance metric, such as the cross-entropy loss, the classification error rate and the negative log-likelihood. In many practical cases, labels are not available in time as labeling itself is a time-consuming and expensive task. To this end, we propose an approach to CNN model selection using only unlabeled data. We develop this method based on a principle termed consistent relative confidence. Experimental results on benchmark datasets demonstrate the effectiveness and efficiency of our method.
Double machine learning (DML) has become an increasingly popular tool for automated variable selection in high-dimensional settings. Even though the ability to deal with a large number of potential covariates can render selection-on-observables assumptions more plausible, there is at the same time a growing risk that endogenous variables are included, which would lead to the violation of conditional independence. This paper demonstrates that DML is very sensitive to the inclusion of only a few "bad controls" in the covariate space. The resulting bias varies with the nature of the theoretical causal model, which raises concerns about the feasibility of selecting control variables in a data-driven way.
While information delivery in industrial Internet of things demands reliability and latency guarantees, the freshness of the controller's available information, measured by the age of information (AoI), is paramount for high-performing industrial automation. The problem in this work is cast as a sensor's transmit power minimization subject to the peak-AoI requirement and a probabilistic constraint on queuing latency. We further characterize the tail behavior of the latency by a generalized Pareto distribution (GPD) for solving the power allocation problem through Lyapunov optimization. As each sensor utilizes its own data to locally train the GPD model, we incorporate federated learning and propose a local-model selection approach which accounts for correlation among the sensor's training data. Numerical results show the tradeoff between the transmit power, peak AoI, and delay's tail distribution. Furthermore, we verify the superiority of the proposed correlation-aware approach for selecting the local models in federated learning over an existing baseline.
With the emergence of light field imaging in recent years, the compression of its elementary image array (EIA) has become a significant problem. Our coding framework includes modeling and reconstruction. For the modeling, the covariance-matrix form of the 4-D Epanechnikov kernel (4-D EK) and its correlated statistics were deduced to obtain the 4-D Epanechnikov mixture models (4-D EMMs). A 4-D Epanechnikov mixture regression (4-D EMR) was proposed based on this 4-D EK, and a 4-D adaptive model selection (4-D AMLS) algorithm was designed to realize the optimal modeling for a pseudo video sequence (PVS) of the extracted key-EIA. A linear function based reconstruction (LFBR) was proposed based on the correlation between adjacent elementary images (EIs). The decoded images realized a clear outline reconstruction and superior coding efficiency compared to high-efficiency video coding (HEVC) and JPEG 2000 below approximately 0.05 bpp. This work realized an unprecedented theoretical application by (1) proposing the 4-D Epanechnikov kernel theory, (2) exploiting the 4-D Epanechnikov mixture regression and its application in the modeling of the pseudo video sequence of light field images, (3) using 4-D adaptive model selection for the optimal number of models, and (4) employing a linear function-based reconstruction according to the content similarity.
The advances in deep neural networks (DNN) have significantly enhanced real-time detection of anomalous data in IoT applications. However, the complexity-accuracy-delay dilemma persists: complex DNN models offer higher accuracy, but typical IoT devices can barely afford the computation load, and the remedy of offloading the load to the cloud incurs long delay. In this paper, we address this challenge by proposing an adaptive anomaly detection scheme with hierarchical edge computing (HEC). Specifically, we first construct multiple anomaly detection DNN models with increasing complexity, and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network. We also incorporate a parallelism policy training method to accelerate the training process by taking advantage of distributed models. We build an HEC testbed using real IoT devices, implement and evaluate our contextual-bandit approach with both univariate and multivariate IoT datasets. In comparison with both baseline and state-of-the-art schemes, our adaptive approach strikes the best accuracy-delay tradeoff on the univariate dataset, and achieves the best accuracy and F1-score on the multivariate dataset with only negligibly longer delay than the best (but inflexible) scheme.
Accurate camera calibration is a precondition for many computer vision applications. Calibration errors, such as wrong model assumptions or imprecise parameter estimation, can deteriorate a system's overall performance, making the reliable detection and quantification of these errors critical. In this work, we introduce an evaluation scheme to capture the fundamental error sources in camera calibration: systematic errors (biases) and uncertainty (variance). The proposed bias detection method uncovers smallest systematic errors and thereby reveals imperfections of the calibration setup and provides the basis for camera model selection. A novel resampling-based uncertainty estimator enables uncertainty estimation under non-ideal conditions and thereby extends the classical covariance estimator. Furthermore, we derive a simple uncertainty metric that is independent of the camera model. In combination, the proposed methods can be used to assess the accuracy of individual calibrations, but also to benchmark new calibration algorithms, camera models, or calibration setups. We evaluate the proposed methods with simulations and real cameras.
Reinforcement learning (RL) can be used to learn treatment policies and aid decision making in healthcare. However, given the need for generalization over complex state/action spaces, the incorporation of function approximators (e.g., deep neural networks) requires model selection to reduce overfitting and improve policy performance at deployment. Yet a standard validation pipeline for model selection requires running a learned policy in the actual environment, which is often infeasible in a healthcare setting. In this work, we investigate a model selection pipeline for offline RL that relies on off-policy evaluation (OPE) as a proxy for validation performance. We present an in-depth analysis of popular OPE methods, highlighting the additional hyperparameters and computational requirements (fitting/inference of auxiliary models) when used to rank a set of candidate policies. We compare the utility of different OPE methods as part of the model selection pipeline in the context of learning to treat patients with sepsis. Among all the OPE methods we considered, fitted Q evaluation (FQE) consistently leads to the best validation ranking, but at a high computational cost. To balance this trade-off between accuracy of ranking and computational efficiency, we propose a simple two-stage approach to accelerate model selection by avoiding potentially unnecessary computation. Our work serves as a practical guide for offline RL model selection and can help RL practitioners select policies using real-world datasets. To facilitate reproducibility and future extensions, the code accompanying this paper is available online at https://github.com/MLD3/OfflineRL_ModelSelection.
This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price changes after their arrivals. To capture the stimulating effects between multiple types of order book events, we use the multivariate Hawkes process to model the self- and mutually-exciting event arrivals. We also integrate a Markovian baseline intensity into the event arrival dynamic, by including the impacts of order book liquidity state and time factor to the baseline intensity. A regression-based non-parametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated in the estimation procedure. Besides, model selection method based on Akaike Information Criteria is applied to evaluate the effect of each part of the proposed model. An implementation example based on real LOB data is provided. Through the example, we study the empirical shapes of Hawkes excitement functions, the effects of liquidity state as well as time factors, the LASSO variable selection, and the explanatory power of Hawkes and Markovian elements to the dynamics of the order book.
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.
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed Monte Carlo (CMC) scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing.
Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony and Sparsity is proposed. A Parsimony Enhanced Sparse Bayesian Learning (PeSBL) method is developed for discovering the governing Partial Differential Equations (PDEs) of nonlinear dynamical systems. Compared with the conventional Sparse Bayesian Learning (SBL) method, the PeSBL method promotes parsimony of the learned model in addition to its sparsity. In this method, the parsimony of model terms is evaluated using their locations in the prescribed candidate library, for the first time, considering the increased complexity with the power of polynomials and the order of spatial derivatives. Subsequently, the model parameters are updated through Bayesian inference with the raw data. This procedure aims to reduce the error associated with the possible loss of information in data preprocessing and numerical differentiation prior to sparse regression. Results of numerical case studies indicate that the governing PDEs of many canonical dynamical systems can be correctly identified using the proposed PeSBL method from highly noisy data (up to 50% in the current study). Next, the proposed methodology is extended for stochastic PDE learning where all parameters and modeling error are considered as random variables. Hierarchical Bayesian Inference (HBI) is integrated with the proposed framework for stochastic PDE learning from a population of observations. Finally, the proposed PeSBL is demonstrated for system response prediction with uncertainties and anomaly diagnosis. Codes of all demonstrated examples in this study are available on the website: https://github.com/ymlasu.
As deep learning becomes more expensive, both in terms of time and compute, inefficiencies in machine learning (ML) training prevent practical usage of state-of-the-art models for most users. The newest model architectures are simply too large to be fit onto a single processor. To address the issue, many ML practitioners have turned to model parallelism as a method of distributing the computational requirements across several devices. Unfortunately, the sequential nature of neural networks causes very low efficiency and device utilization in model parallel training jobs. We propose a new form of "shard parallelism" combining task and model parallelism, then package it into a framework we name Hydra. Hydra recasts the problem of model parallelism in the multi-model context to produce a fine-grained parallel workload of independent model shards, rather than independent models. This new parallel design promises dramatic speedups relative to the traditional model parallelism paradigm.
The Jeffreys divergence is a renown symmetrization of the oriented Kullback-Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various techniques with pros and cons have been proposed in the literature to either estimate, approximate, or lower and upper bound this divergence. In this paper, we propose a simple yet fast heuristic to approximate the Jeffreys divergence between two univariate Gaussian mixtures with arbitrary number of components. Our heuristic relies on converting the mixtures into pairs of dually parameterized probability densities belonging to an exponential family. In particular, we consider the versatile polynomial exponential family densities, and design a divergence to measure in closed-form the goodness of fit between a Gaussian mixture and its polynomial exponential density approximation. This goodness-of-fit divergence is a generalization of the Hyv\"arinen divergence used to estimate models with computationally intractable normalizers. It allows us to perform model selection by choosing the orders of the polynomial exponential densities used to approximate the mixtures. We demonstrate experimentally that our heuristic to approximate the Jeffreys divergence improves by several orders of magnitude the computational time of stochastic Monte Carlo estimations while approximating reasonably well the Jeffreys divergence, specially when the mixtures have a very small number of modes. Besides, our mixture-to-exponential family conversion techniques may prove useful in other settings.
We address the problem of model selection for the finite horizon episodic Reinforcement Learning (RL) problem where the transition kernel $P^*$ belongs to a family of models $\mathcal{P}^*$ with finite metric entropy. In the model selection framework, instead of $\mathcal{P}^*$, we are given $M$ nested families of transition kernels $\cP_1 \subset \cP_2 \subset \ldots \subset \cP_M$. We propose and analyze a novel algorithm, namely \emph{Adaptive Reinforcement Learning (General)} (\texttt{ARL-GEN}) that adapts to the smallest such family where the true transition kernel $P^*$ lies. \texttt{ARL-GEN} uses the Upper Confidence Reinforcement Learning (\texttt{UCRL}) algorithm with value targeted regression as a blackbox and puts a model selection module at the beginning of each epoch. Under a mild separability assumption on the model classes, we show that \texttt{ARL-GEN} obtains a regret of $\Tilde{\mathcal{O}}(d_{\mathcal{E}}^*H^2+\sqrt{d_{\mathcal{E}}^* \mathbb{M}^* H^2 T})$, with high probability, where $H$ is the horizon length, $T$ is the total number of steps, $d_{\mathcal{E}}^*$ is the Eluder dimension and $\mathbb{M}^*$ is the metric entropy corresponding to $\mathcal{P}^*$. Note that this regret scaling matches that of an oracle that knows $\mathcal{P}^*$ in advance. We show that the cost of model selection for \texttt{ARL-GEN} is an additive term in the regret having a weak dependence on $T$. Subsequently, we remove the separability assumption and consider the setup of linear mixture MDPs, where the transition kernel $P^*$ has a linear function approximation. With this low rank structure, we propose novel adaptive algorithms for model selection, and obtain (order-wise) regret identical to that of an oracle with knowledge of the true model class.
Subspace-valued functions arise in a wide range of problems, including parametric reduced order modeling (PROM). In PROM, each parameter point can be associated with a subspace, which is used for Petrov-Galerkin projections of large system matrices. Previous efforts to approximate such functions use interpolations on manifolds, which can be inaccurate and slow. To tackle this, we propose a novel Bayesian nonparametric model for subspace prediction: the Gaussian Process Subspace regression (GPS) model. This method is extrinsic and intrinsic at the same time: with multivariate Gaussian distributions on the Euclidean space, it induces a joint probability model on the Grassmann manifold, the set of fixed-dimensional subspaces. The GPS adopts a simple yet general correlation structure, and a principled approach for model selection. Its predictive distribution admits an analytical form, which allows for efficient subspace prediction over the parameter space. For PROM, the GPS provides a probabilistic prediction at a new parameter point that retains the accuracy of local reduced models, at a computational complexity that does not depend on system dimension, and thus is suitable for online computation. We give four numerical examples to compare our method to subspace interpolation, as well as two methods that interpolate local reduced models. Overall, GPS is the most data efficient, more computationally efficient than subspace interpolation, and gives smooth predictions with uncertainty quantification.
We consider the problem of model selection for the general stochastic contextual bandits under the realizability assumption. We propose a successive refinement based algorithm called Adaptive Contextual Bandit ({\ttfamily ACB}), that works in phases and successively eliminates model classes that are too simple to fit the given instance. We prove that this algorithm is adaptive, i.e., the regret rate order-wise matches that of any provable contextual bandit algorithm (ex. \cite{falcon}), that needs the knowledge of the true model class. The price of not knowing the correct model class turns out to be only an additive term contributing to the second order term in the regret bound. This cost possess the intuitive property that it becomes smaller as the model class becomes easier to identify, and vice-versa. We also show that a much simpler explore-then-commit (ETC) style algorithm also obtains similar regret bound, despite not knowing the true model class. However, the cost of model selection is higher in ETC as opposed to in {\ttfamily ACB}, as expected. Furthermore, for the special case of linear contextual bandits, we propose specialized algorithms that obtain sharper guarantees compared to the generic setup.
Attributed event sequences are commonly encountered in practice. A recent research line focuses on incorporating neural networks with the statistical model -- marked point processes, which is the conventional tool for dealing with attributed event sequences. Neural marked point processes possess good interpretability of probabilistic models as well as the representational power of neural networks. However, we find that performance of neural marked point processes is not always increasing as the network architecture becomes more complicated and larger, which is what we call the performance saturation phenomenon. This is due to the fact that the generalization error of neural marked point processes is determined by both the network representational ability and the model specification at the same time. Therefore we can draw two major conclusions: first, simple network structures can perform no worse than complicated ones for some cases; second, using a proper probabilistic assumption is as equally, if not more, important as improving the complexity of the network. Based on this observation, we propose a simple graph-based network structure called GCHP, which utilizes only graph convolutional layers, thus it can be easily accelerated by the parallel mechanism. We directly consider the distribution of interarrival times instead of imposing a specific assumption on the conditional intensity function, and propose to use a likelihood ratio loss with a moment matching mechanism for optimization and model selection. Experimental results show that GCHP can significantly reduce training time and the likelihood ratio loss with interarrival time probability assumptions can greatly improve the model performance.
While many real-world data streams imply that they change frequently in a nonstationary way, most of deep learning methods optimize neural networks on training data, and this leads to severe performance degradation when dataset shift happens. However, it is less possible to annotate or inspect newly streamed data by humans, and thus it is desired to measure model drift at inference time in an unsupervised manner. In this paper, we propose a novel method of model drift estimation by exploiting statistics of batch normalization layer on unlabeled test data. To remedy possible sampling error of streamed input data, we adopt low-rank approximation to each representational layer. We show the effectiveness of our method not only on dataset shift detection but also on model selection when there are multiple candidate models among model zoo or training trajectories in an unsupervised way. We further demonstrate the consistency of our method by comparing model drift scores between different network architectures.
Bayesian formulations of deep learning have been shown to have compelling theoretical properties and offer practical functional benefits, such as improved predictive uncertainty quantification and model selection. The Laplace approximation (LA) is a classic, and arguably the simplest family of approximations for the intractable posteriors of deep neural networks. Yet, despite its simplicity, the LA is not as popular as alternatives like variational Bayes or deep ensembles. This may be due to assumptions that the LA is expensive due to the involved Hessian computation, that it is difficult to implement, or that it yields inferior results. In this work we show that these are misconceptions: we (i) review the range of variants of the LA including versions with minimal cost overhead; (ii) introduce "laplace", an easy-to-use software library for PyTorch offering user-friendly access to all major flavors of the LA; and (iii) demonstrate through extensive experiments that the LA is competitive with more popular alternatives in terms of performance, while excelling in terms of computational cost. We hope that this work will serve as a catalyst to a wider adoption of the LA in practical deep learning, including in domains where Bayesian approaches are not typically considered at the moment.
Lyme disease which is one of the most common infectious vector-borne diseases manifests itself in most cases with erythema migrans (EM) skin lesions. Recent studies show that convolutional neural networks (CNNs) perform well to identify skin lesions from images. Lightweight CNN based pre-scanner applications for resource-constrained mobile devices can help users with early diagnosis of Lyme disease and prevent the transition to a severe late form thanks to appropriate antibiotic therapy. Also, resource-intensive CNN based robust computer applications can assist non-expert practitioners with an accurate diagnosis. The main objective of this study is to extensively analyze the effectiveness of CNNs for diagnosing Lyme disease from images and to find out the best CNN architectures considering resource constraints. First, we created an EM dataset with the help of expert dermatologists from Clermont-Ferrand University Hospital Center of France. Second, we benchmarked this dataset for twenty-three CNN architectures customized from VGG, ResNet, DenseNet, MobileNet, Xception, NASNet, and EfficientNet architectures in terms of predictive performance, computational complexity, and statistical significance. Third, to improve the performance of the CNNs, we used custom transfer learning from ImageNet pre-trained models as well as pre-trained the CNNs with the skin lesion dataset HAM10000. Fourth, for model explainability, we utilized Gradient-weighted Class Activation Mapping to visualize the regions of input that are significant to the CNNs for making predictions. Fifth, we provided guidelines for model selection based on predictive performance and computational complexity.