Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in finite horizon scenarios, where input lengths are finite, determining the optimal stopping rule becomes computationally intensive due to the need for backward induction, limiting practical applicability. We thus introduce FIRMBOUND, an SPRT-based framework that efficiently estimates the solution to backward induction from training data, bridging the gap between optimal stopping theory and real-world deployment. It employs density ratio estimation and convex function learning to provide statistically consistent estimators for sufficient statistic and conditional expectation, both essential for solving backward induction; consequently, FIRMBOUND minimizes Bayes risk to reach optimality. Additionally, we present a faster alternative using Gaussian process regression, which significantly reduces training time while retaining low deployment overhead, albeit with potential compromise in statistical consistency. Experiments across independent and identically distributed (i.i.d.), non-i.i.d., binary, multiclass, synthetic, and real-world datasets show that FIRMBOUND achieves optimalities in the sense of Bayes risk and speed-accuracy tradeoff. Furthermore, it advances the tradeoff boundary toward optimality when possible and reduces decision-time variance, ensuring reliable decision-making. Code is publicly available at https://github.com/Akinori-F-Ebihara/FIRMBOUND
\texttt{ml\_edm} is a Python 3 library, designed for early decision making of any learning tasks involving temporal/sequential data. The package is also modular, providing researchers an easy way to implement their own triggering strategy for classification, regression or any machine learning task. As of now, many Early Classification of Time Series (ECTS) state-of-the-art algorithms, are efficiently implemented in the library leveraging parallel computation. The syntax follows the one introduce in \texttt{scikit-learn}, making estimators and pipelines compatible with \texttt{ml\_edm}. This software is distributed over the BSD-3-Clause license, source code can be found at \url{https://github.com/ML-EDM/ml_edm}.
In many situations, the measurements of a studied phenomenon are provided sequentially, and the prediction of its class needs to be made as early as possible so as not to incur too high a time penalty, but not too early and risk paying the cost of misclassification. This problem has been particularly studied in the case of time series, and is known as Early Classification of Time Series (ECTS). Although it has been the subject of a growing body of literature, there is still a lack of a systematic, shared evaluation protocol to compare the relative merits of the various existing methods. This document begins by situating these methods within a principle-based taxonomy. It defines dimensions for organizing their evaluation, and then reports the results of a very extensive set of experiments along these dimensions involving nine state-of-the art ECTS algorithms. In addition, these and other experiments can be carried out using an open-source library in which most of the existing ECTS algorithms have been implemented (see https://github.com/ML-EDM/ml_edm).
Key-value sequence data has become ubiquitous and naturally appears in a variety of real-world applications, ranging from the user-product purchasing sequences in e-commerce, to network packet sequences forwarded by routers in networking. Classifying these key-value sequences is important in many scenarios such as user profiling and malicious applications identification. In many time-sensitive scenarios, besides the requirement of classifying a key-value sequence accurately, it is also desired to classify a key-value sequence early, in order to respond fast. However, these two goals are conflicting in nature, and it is challenging to achieve them simultaneously. In this work, we formulate a novel tangled key-value sequence early classification problem, where a tangled key-value sequence is a mixture of several concurrent key-value sequences with different keys. The goal is to classify each individual key-value sequence sharing a same key both accurately and early. To address this problem, we propose a novel method, i.e., Key-Value sequence Early Co-classification (KVEC), which leverages both inner- and inter-correlations of items in a tangled key-value sequence through key correlation and value correlation to learn a better sequence representation. Meanwhile, a time-aware halting policy decides when to stop the ongoing key-value sequence and classify it based on current sequence representation. Experiments on both real-world and synthetic datasets demonstrate that our method outperforms the state-of-the-art baselines significantly. KVEC improves the prediction accuracy by up to $4.7 - 17.5\%$ under the same prediction earliness condition, and improves the harmonic mean of accuracy and earliness by up to $3.7 - 14.0\%$.
Deep learning (DL) has been successfully applied to encrypted network traffic classification in experimental settings. However, in production use, it has been shown that a DL classifier's performance inevitably decays over time. Re-training the model on newer datasets has been shown to only partially improve its performance. Manually re-tuning the model architecture to meet the performance expectations on newer datasets is time-consuming and requires domain expertise. We propose AutoML4ETC, a novel tool to automatically design efficient and high-performing neural architectures for encrypted traffic classification. We define a novel, powerful search space tailored specifically for the early classification of encrypted traffic using packet header bytes. We show that with different search strategies over our search space, AutoML4ETC generates neural architectures that outperform the state-of-the-art encrypted traffic classifiers on several datasets, including public benchmark datasets and real-world TLS and QUIC traffic collected from the Orange mobile network. In addition to being more accurate, AutoML4ETC's architectures are significantly more efficient and lighter in terms of the number of parameters. Finally, we make AutoML4ETC publicly available for future research.
Nowadays, the deployment of deep learning models on edge devices for addressing real-world classification problems is becoming more prevalent. Moreover, there is a growing popularity in the approach of early classification, a technique that involves classifying the input data after observing only an early portion of it, aiming to achieve reduced communication and computation requirements, which are crucial parameters in edge intelligence environments. While early classification in the field of time series analysis has been broadly researched, existing solutions for multivariate time series problems primarily focus on early classification along the temporal dimension, treating the multiple input channels in a collective manner. In this study, we propose a more flexible early classification pipeline that offers a more granular consideration of input channels and extends the early classification paradigm to the channel dimension. To implement this method, we utilize reinforcement learning techniques and introduce constraints to ensure the feasibility and practicality of our objective. To validate its effectiveness, we conduct experiments using synthetic data and we also evaluate its performance on real datasets. The comprehensive results from our experiments demonstrate that, for multiple datasets, our method can enhance the early classification paradigm by achieving improved accuracy for equal input utilization.
Early exiting has become a promising approach to improving the inference efficiency of deep networks. By structuring models with multiple classifiers (exits), predictions for ``easy'' samples can be generated at earlier exits, negating the need for executing deeper layers. Current multi-exit networks typically implement linear classifiers at intermediate layers, compelling low-level features to encapsulate high-level semantics. This sub-optimal design invariably undermines the performance of later exits. In this paper, we propose Dynamic Perceiver (Dyn-Perceiver) to decouple the feature extraction procedure and the early classification task with a novel dual-branch architecture. A feature branch serves to extract image features, while a classification branch processes a latent code assigned for classification tasks. Bi-directional cross-attention layers are established to progressively fuse the information of both branches. Early exits are placed exclusively within the classification branch, thus eliminating the need for linear separability in low-level features. Dyn-Perceiver constitutes a versatile and adaptable framework that can be built upon various architectures. Experiments on image classification, action recognition, and object detection demonstrate that our method significantly improves the inference efficiency of different backbones, outperforming numerous competitive approaches across a broad range of computational budgets. Evaluation on both CPU and GPU platforms substantiate the superior practical efficiency of Dyn-Perceiver. Code is available at https://www.github.com/LeapLabTHU/Dynamic_Perceiver.
Theoretically-inspired sequential density ratio estimation (SDRE) algorithms are proposed for the early classification of time series. Conventional SDRE algorithms can fail to estimate DRs precisely due to the internal overnormalization problem, which prevents the DR-based sequential algorithm, Sequential Probability Ratio Test (SPRT), from reaching its asymptotic Bayes optimality. Two novel SPRT-based algorithms, B2Bsqrt-TANDEM and TANDEMformer, are designed to avoid the overnormalization problem for precise unsupervised regression of SDRs. The two algorithms statistically significantly reduce DR estimation errors and classification errors on an artificial sequential Gaussian dataset and real datasets (SiW, UCF101, and HMDB51), respectively. The code is available at: https://github.com/Akinori-F-Ebihara/LLR_saturation_problem.
Early classification algorithms help users react faster to their machine learning model's predictions. Early warning systems in hospitals, for example, let clinicians improve their patients' outcomes by accurately predicting infections. While early classification systems are advancing rapidly, a major gap remains: existing systems do not consider irregular time series, which have uneven and often-long gaps between their observations. Such series are notoriously pervasive in impactful domains like healthcare. We bridge this gap and study early classification of irregular time series, a new setting for early classifiers that opens doors to more real-world problems. Our solution, Stop&Hop, uses a continuous-time recurrent network to model ongoing irregular time series in real time, while an irregularity-aware halting policy, trained with reinforcement learning, predicts when to stop and classify the streaming series. By taking real-valued step sizes, the halting policy flexibly decides exactly when to stop ongoing series in real time. This way, Stop&Hop seamlessly integrates information contained in the timing of observations, a new and vital source for early classification in this setting, with the time series values to provide early classifications for irregular time series. Using four synthetic and three real-world datasets, we demonstrate that Stop&Hop consistently makes earlier and more-accurate predictions than state-of-the-art alternatives adapted to this new problem. Our code is publicly available at https://github.com/thartvigsen/StopAndHop.
In recent years, deep learning has successfully been applied to automate a wide variety of tasks in diagnostic histopathology. However, fast and reliable localization of small-scale regions-of-interest (ROI) has remained a key challenge, as discriminative morphologic features often occupy only a small fraction of a gigapixel-scale whole-slide image (WSI). In this paper, we propose a sparse WSI analysis method for the rapid identification of high-power ROI for WSI-level classification. We develop an evaluation framework inspired by the early classification literature, in order to quantify the tradeoff between diagnostic performance and inference time for sparse analytic approaches. We test our method on a common but time-consuming task in pathology - that of diagnosing gastric intestinal metaplasia (GIM) on hematoxylin and eosin (H&E)-stained slides from endoscopic biopsy specimens. GIM is a well-known precursor lesion along the pathway to development of gastric cancer. We performed a thorough evaluation of the performance and inference time of our approach on a test set of GIM-positive and GIM-negative WSI, finding that our method successfully detects GIM in all positive WSI, with a WSI-level classification area under the receiver operating characteristic curve (AUC) of 0.98 and an average precision (AP) of 0.95. Furthermore, we show that our method can attain these metrics in under one minute on a standard CPU. Our results are applicable toward the goal of developing neural networks that can easily be deployed in clinical settings to support pathologists in quickly localizing and diagnosing small-scale morphologic features in WSI.
We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. The matrix sequential probability ratio test (MSPRT) is known to be asymptotically optimal for this setting, but contains a critical assumption that hinders broad real-world applications; the MSPRT requires the underlying probability density. To address this problem, we propose to solve density ratio matrix estimation (DRME), a novel type of density ratio estimation that consists of estimating matrices of multiple density ratios with constraints and thus is more challenging than the conventional density ratio estimation. We propose a log-sum-exp-type loss function (LSEL) for solving DRME and prove the following: (i) the LSEL provides the true density ratio matrix as the sample size of the training set increases (consistency); (ii) it assigns larger gradients to harder classes (hard class weighting effect); and (iii) it provides discriminative scores even on class-imbalanced datasets (guess-aversion). Our overall architecture for early classification, MSPRT-TANDEM, statistically significantly outperforms baseline models on four datasets including action recognition, especially in the early stage of sequential observations. Our code and datasets are publicly available at: https://github.com/TaikiMiyagawa/MSPRT-TANDEM.
Sequence classification is the task of predicting a class label given a sequence of observations. In many applications such as healthcare monitoring or intrusion detection, early classification is crucial to prompt intervention. In this work, we learn sequence classifiers that favour early classification from an evolving observation trace. While many state-of-the-art sequence classifiers are neural networks, and in particular LSTMs, our classifiers take the form of finite state automata and are learned via discrete optimization. Our automata-based classifiers are interpretable---supporting explanation, counterfactual reasoning, and human-in-the-loop modification---and have strong empirical performance. Experiments over a suite of goal recognition and behaviour classification datasets show our learned automata-based classifiers to have comparable test performance to LSTM-based classifiers, with the added advantage of being interpretable.
Remote sensing satellites capture the cyclic dynamics of our Planet in regular time intervals recorded in satellite time series data. End-to-end trained deep learning models use this time series data to make predictions at a large scale, for instance, to produce up-to-date crop cover maps. Most time series classification approaches focus on the accuracy of predictions. However, the earliness of the prediction is also of great importance since coming to an early decision can make a crucial difference in time-sensitive applications. In this work, we present an End-to-End Learned Early Classification of Time Series (ELECTS) model that estimates a classification score and a probability of whether sufficient data has been observed to come to an early and still accurate decision. ELECTS is modular: any deep time series classification model can adopt the ELECTS conceptual idea by adding a second prediction head that outputs a probability of stopping the classification. The ELECTS loss function then optimizes the overall model on a balanced objective of earliness and accuracy. Our experiments on four crop classification datasets from Europe and Africa show that ELECTS allows reaching state-of-the-art accuracy while reducing the quantity of data massively to be downloaded, stored, and processed. The source code is available at https://github.com/marccoru/elects.