Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence network among the dimensions of multi-dimensional temporal processes is of high importance in disciplines where a high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multi-dimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method incausal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts knowledge.
Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of latent confounders. This task requires solutions that come from different areas of statistics and machine learning. We combine elements of variational Bayesian methods, expectation-maximisation, hill-climbing search, and structure learning under the assumption of causal insufficiency. We propose two learning strategies; one that maximises model selection accuracy, and another that improves computational efficiency in exchange for minor reductions in accuracy. The former strategy is suitable for small networks and the latter for moderate size networks. Both learning strategies perform well relative to existing solutions.
Knowledge distillation (KD) has shown very promising capabilities in transferring learning representations from large models (teachers) to small models (students). However, as the capacity gap between students and teachers becomes larger, existing KD methods fail to achieve better results. Our work shows that the `prior knowledge' is vital to KD, especially when applying large teachers. Particularly, we propose the dynamic prior knowledge (DPK), which integrates part of teacher's features as the prior knowledge before the feature distillation. This means that our method also takes the teacher's feature as `input', not just `target'. Besides, we dynamically adjust the ratio of the prior knowledge during the training phase according to the feature gap, thus guiding the student in an appropriate difficulty. To evaluate the proposed method, we conduct extensive experiments on two image classification benchmarks (i.e. CIFAR100 and ImageNet) and an object detection benchmark (i.e. MS COCO. The results demonstrate the superiority of our method in performance under varying settings. Besides, our DPK makes the performance of the student model positively correlated with that of the teacher model, which means that we can further boost the accuracy of students by applying larger teachers. More importantly, DPK provides a fast solution in teacher model selection for any given model.
Equality of opportunity has emerged as an important ideal of distributive justice. Empirically, Inequality of Opportunity (IOp) is measured in two steps: first, an outcome (e.g., income) is predicted given individual circumstances; and second, an inequality index (e.g., Gini) of the predictions is computed. Machine Learning (ML) methods are tremendously useful in the first step. However, they can cause sizable biases in IOp since the bias-variance trade-off allows the bias to creep in the second step. We propose a simple debiased IOp estimator robust to such ML biases and provide the first valid inferential theory for IOp. We demonstrate improved performance in simulations and report the first unbiased measures of income IOp in Europe. Mother's education and father's occupation are the circumstances that explain the most. Plug-in estimators are very sensitive to the ML algorithm, while debiased IOp estimators are robust. These results are extended to a general U-statistics setting.
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.
Automated machine learning (AutoML) frameworks have become important tools in the data scientists' arsenal, as they dramatically reduce the manual work devoted to the construction of ML pipelines. Such frameworks intelligently search among millions of possible ML pipelines - typically containing feature engineering, model selection and hyper parameters tuning steps - and finally output an optimal pipeline in terms of predictive accuracy. However, when the dataset is large, each individual configuration takes longer to execute, therefore the overall AutoML running times become increasingly high. To this end, we present SubStrat, an AutoML optimization strategy that tackles the data size, rather than configuration space. It wraps existing AutoML tools, and instead of executing them directly on the entire dataset, SubStrat uses a genetic-based algorithm to find a small yet representative data subset which preserves a particular characteristic of the full data. It then employs the AutoML tool on the small subset, and finally, it refines the resulted pipeline by executing a restricted, much shorter, AutoML process on the large dataset. Our experimental results, performed on two popular AutoML frameworks, Auto-Sklearn and TPOT, show that SubStrat reduces their running times by 79% (on average), with less than 2% average loss in the accuracy of the resulted ML pipeline.
Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.
We consider prediction with expert advice for strongly convex and bounded losses, and investigate trade-offs between regret and "variance" (i.e., squared difference of learner's predictions and best expert predictions). With $K$ experts, the Exponentially Weighted Average (EWA) algorithm is known to achieve $O(\log K)$ regret. We prove that a variant of EWA either achieves a negative regret (i.e., the algorithm outperforms the best expert), or guarantees a $O(\log K)$ bound on both variance and regret. Building on this result, we show several examples of how variance of predictions can be exploited in learning. In the online to batch analysis, we show that a large empirical variance allows to stop the online to batch conversion early and outperform the risk of the best predictor in the class. We also recover the optimal rate of model selection aggregation when we do not consider early stopping. In online prediction with corrupted losses, we show that the effect of corruption on the regret can be compensated by a large variance. In online selective sampling, we design an algorithm that samples less when the variance is large, while guaranteeing the optimal regret bound in expectation. In online learning with abstention, we use a similar term as the variance to derive the first high-probability $O(\log K)$ regret bound in this setting. Finally, we extend our results to the setting of online linear regression.
This paper presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture's integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.
We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent ``particles'', where each particle is described by its spatial location and features of its surrounding region. To drive learning of such representations, we follow a VAE-based approach and introduce a prior for particle positions based on a spatial-softmax architecture, and a modification of the evidence lower bound loss inspired by the Chamfer distance between particles. We demonstrate that our DLP representations are useful for downstream tasks such as unsupervised keypoint (KP) detection, image manipulation, and video prediction for scenes composed of multiple dynamic objects. In addition, we show that our probabilistic interpretation of the problem naturally provides uncertainty estimates for particle locations, which can be used for model selection, among other tasks. Videos and code are available: https://taldatech.github.io/deep-latent-particles-web/
Deploying machine learning models to new tasks is a major challenge despite the large size of the modern training datasets. However, it is conceivable that the training data can be reweighted to be more representative of the new (target) task. We consider the problem of reweighing the training samples to gain insights into the distribution of the target task. Specifically, we formulate a distribution shift model based on the exponential tilt assumption and learn train data importance weights minimizing the KL divergence between labeled train and unlabeled target datasets. The learned train data weights can then be used for downstream tasks such as target performance evaluation, fine-tuning, and model selection. We demonstrate the efficacy of our method on Waterbirds and Breeds benchmarks.
Deep reinforcement learning (DRL) has become a dominant deep-learning paradigm for tasks where complex policies are learned within reactive systems. Unfortunately, these policies are known to be susceptible to bugs. Despite significant progress in DNN verification, there has been little work demonstrating the use of modern verification tools on real-world, DRL-controlled systems. In this case study, we attempt to begin bridging this gap, and focus on the important task of mapless robotic navigation -- a classic robotics problem, in which a robot, usually controlled by a DRL agent, needs to efficiently and safely navigate through an unknown arena towards a target. We demonstrate how modern verification engines can be used for effective model selection, i.e., selecting the best available policy for the robot in question from a pool of candidate policies. Specifically, we use verification to detect and rule out policies that may demonstrate suboptimal behavior, such as collisions and infinite loops. We also apply verification to identify models with overly conservative behavior, thus allowing users to choose superior policies, which might be better at finding shorter paths to a target. To validate our work, we conducted extensive experiments on an actual robot, and confirmed that the suboptimal policies detected by our method were indeed flawed. We also demonstrate the superiority of our verification-driven approach over state-of-the-art, gradient attacks. Our work is the first to establish the usefulness of DNN verification in identifying and filtering out suboptimal DRL policies in real-world robots, and we believe that the methods presented here are applicable to a wide range of systems that incorporate deep-learning-based agents.
Research in massively multilingual image captioning has been severely hampered by a lack of high-quality evaluation datasets. In this paper we present the Crossmodal-3600 dataset (XM3600 in short), a geographically diverse set of 3600 images annotated with human-generated reference captions in 36 languages. The images were selected from across the world, covering regions where the 36 languages are spoken, and annotated with captions that achieve consistency in terms of style across all languages, while avoiding annotation artifacts due to direct translation. We apply this benchmark to model selection for massively multilingual image captioning models, and show superior correlation results with human evaluations when using XM3600 as golden references for automatic metrics.
Organizations leverage anomaly and changepoint detection algorithms to detect changes in user behavior or service availability and performance. Many off-the-shelf detection algorithms, though effective, cannot readily be used in large organizations where thousands of users monitor millions of use cases and metrics with varied time series characteristics and anomaly patterns. The selection of algorithm and parameters needs to be precise for each use case: manual tuning does not scale, and automated tuning requires ground truth, which is rarely available. In this paper, we explore MOSPAT, an end-to-end automated machine learning based approach for model and parameter selection, combined with a generative model to produce labeled data. Our scalable end-to-end system allows individual users in large organizations to tailor time-series monitoring to their specific use case and data characteristics, without expert knowledge of anomaly detection algorithms or laborious manual labeling. Our extensive experiments on real and synthetic data demonstrate that this method consistently outperforms using any single algorithm.
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize the distance between the subspaces of all data, so that subspaces of the same cluster get {\em fused} together. Our method allows low, high, and even full-rank data; it directly accounts for noise, and its sample complexity approaches the information-theoretic limit. In addition, our approach provides a natural model selection {\em clusterpath}, and a direct completion method. We give convergence guarantees, analyze computational complexity, and show through extensive experiments on real and synthetic data that our approach performs comparably to the state-of-the-art with complete data, and dramatically better if data is missing.
We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.
Time series anomaly detection has been recognized as of critical importance for the reliable and efficient operation of real-world systems. Many anomaly detection methods have been developed based on various assumptions on anomaly characteristics. However, due to the complex nature of real-world data, different anomalies within a time series usually have diverse profiles supporting different anomaly assumptions. This makes it difficult to find a single anomaly detector that can consistently outperform other models. In this work, to harness the benefits of different base models, we propose a reinforcement learning-based model selection framework. Specifically, we first learn a pool of different anomaly detection models, and then utilize reinforcement learning to dynamically select a candidate model from these base models. Experiments on real-world data have demonstrated that the proposed strategy can indeed outplay all baseline models in terms of overall performance.
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and make decision around them. Neural networks are now consistently used as universal function approximators for data with underlying mechanisms that are incompletely understood or exceedingly complex. However, neural networks alone ignore the fundamental laws of physics and often fail to make plausible predictions. Here we integrate data, physics, and uncertainties by combining neural networks, physics-informed modeling, and Bayesian inference to improve the predictive potential of traditional neural network models. We embed the physical model of a damped harmonic oscillator into a fully-connected feed-forward neural network to explore a simple and illustrative model system, the outbreak dynamics of COVID-19. Our Physics-Informed Neural Networks can seamlessly integrate data and physics, robustly solve forward and inverse problems, and perform well for both interpolation and extrapolation, even for a small amount of noisy and incomplete data. At only minor additional cost, they can self-adaptively learn the weighting between data and physics. Combined with Bayesian Neural Networks, they can serve as priors in a Bayesian Inference, and provide credible intervals for uncertainty quantification. Our study reveals the inherent advantages and disadvantages of Neural Networks, Bayesian Inference, and a combination of both and provides valuable guidelines for model selection. While we have only demonstrated these approaches for the simple model problem of a seasonal endemic infectious disease, we anticipate that the underlying concepts and trends generalize to more complex disease conditions and, more broadly, to a wide variety of nonlinear dynamical systems.
With the advent of ubiquitous deployment of smart devices and the Internet of Things, data sources for machine learning inference have increasingly moved to the edge of the network. Existing machine learning inference platforms typically assume a homogeneous infrastructure and do not take into account the more complex and tiered computing infrastructure that includes edge devices, local hubs, edge datacenters, and cloud datacenters. On the other hand, recent AutoML efforts have provided viable solutions for model compression, pruning and quantization for heterogeneous environments; for a machine learning model, now we may easily find or even generate a series of models with different tradeoffs between accuracy and efficiency. We design and implement JellyBean, a system for serving and optimizing machine learning inference workflows on heterogeneous infrastructures. Given service-level objectives (e.g., throughput, accuracy), JellyBean picks the most cost-efficient models that meet the accuracy target and decides how to deploy them across different tiers of infrastructures. Evaluations show that JellyBean reduces the total serving cost of visual question answering by up to 58%, and vehicle tracking from the NVIDIA AI City Challenge by up to 36% compared with state-of-the-art model selection and worker assignment solutions. JellyBean also outperforms prior ML serving systems (e.g., Spark on the cloud) up to 5x in serving costs.
This paper contributes to interpretable machine learning via visual knowledge discovery in general line coordinates (GLC). The concepts of hyperblocks as interpretable dataset units and general line coordinates are combined to create a visual self-service machine learning model. The DSC1 and DSC2 lossless multidimensional coordinate systems are proposed. DSC1 and DSC2 can map multiple dataset attributes to a single two-dimensional (X, Y) Cartesian plane using a graph construction algorithm. The hyperblock analysis was used to determine visually appealing dataset attribute orders and to reduce line occlusion. It is shown that hyperblocks can generalize decision tree rules and a series of DSC1 or DSC2 plots can visualize a decision tree. The DSC1 and DSC2 plots were tested on benchmark datasets from the UCI ML repository. They allowed for visual classification of data. Additionally, areas of hyperblock impurity were discovered and used to establish dataset splits that highlight the upper estimate of worst-case model accuracy to guide model selection for high-risk decision-making. Major benefits of DSC1 and DSC2 is their highly interpretable nature. They allow domain experts to control or establish new machine learning models through visual pattern discovery.