Analyzing surgical workflow is crucial for computers to understand surgeries. Deep learning techniques have recently been widely applied to recognize surgical workflows. Many of the existing temporal neural network models are limited in their capability to handle long-term dependencies in the data, instead of relying upon strong performance of the underlying per-frame visual models. We propose a new temporal network structure that leverages task-specific network representation to collect long-term sufficient statistics that are propagated by a sufficient statistics model (SSM). We leverage our approach within an LSTM back-bone for the task of surgical phase recognition and explore several choices for propagated statistics. We demonstrate superior results over existing state-of-the-art segmentation and novel segmentation techniques, on two laparoscopic cholecystectomy datasets: the already published Cholec80dataset and MGH100, a novel dataset with more challenging, yet clinically meaningful, segment labels.

Signal Temporal Logic (STL) [14] is gaining momentum as a requirement specification language for complex systems and, in particular, Cyber-Physical Systems [4]. STL has been applied in several flavours, from Runtime-monitoring [4] to control synthesis [10] and falsification problems [9], and recently also within learning algorithms, trying to find a maximally discriminating formula between sets of trajectories [5, 3, 16]. In these applications, a central role is played by the real-valued quantitative semantics [8], measuring robustness of satisfaction. Most of the applications of STL have been applied to deterministic (hybrid) systems, with less emphasis on non-deterministic or stochastic ones [2]. Another area in which formal methods are providing interesting tools is in logic-based distances between models, like bisimulation metrics for Markov models [1], which are typically based on a branching logic. In fact, extending these ideas to linear time logic is hard [7], and typically requires statistical approximations.

Current deep learning research is dominated by benchmark evaluation. A method is regarded as favorable if it empirically performs well on the dedicated test set. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving sets of benchmark data are investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten due to the iterative parameter updates. However, comparison of individual methods is nevertheless treated in isolation from real world application and typically judged by monitoring accumulated test set performance. The closed world assumption remains predominant. It is assumed that during deployment a model is guaranteed to encounter data that stems from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown instances and break down in the face of corrupted data. In this work we argue that notable lessons from open set recognition, the identification of statistically deviating data outside of the observed dataset, and the adjacent field of active learning, where data is incrementally queried such that the expected performance gain is maximized, are frequently overlooked in the deep learning era. Based on these forgotten lessons, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Our results show that this not only benefits each individual paradigm, but highlights the natural synergies in a common framework. We empirically demonstrate improvements when alleviating catastrophic forgetting, querying data in active learning, selecting task orders, while exhibiting robust open world application where previously proposed methods fail.

This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre).

Bayesian is interactive representations of probabilistic interactions between a number of variables. They were designed to ease the presumption of independence in the Naïve Bayes and thus allow for the dependency of variables. The first example, assume I need to see whether God exists. Initially, I have to concur with some techniques to quantify it. Something like'in the event that God existed, at that point harmony, ought to be multiple times more probable than war'.

Machine learning and data mining algorithms play important roles in designing intrusion detection systems. Based on their approaches toward the detection of attacks in a network, intrusion detection systems can be broadly categorized into two types. In the misuse detection systems, an attack in a system is detected whenever the sequence of activities in the network matches with a known attack signature. In the anomaly detection approach, on the other hand, anomalous states in a system are identified based on a significant difference in the state transitions of the system from its normal states. This chapter presents a comprehensive discussion on some of the existing schemes of intrusion detection based on misuse detection, anomaly detection and hybrid detection approaches. Some future directions of research in the design of algorithms for intrusion detection are also identified.

In supervised learning, we fit a single statistical model to a given data set, assuming that the data is associated with a singular task, which yields well-tuned models for specific use, but does not adapt well to new contexts. By contrast, in meta-learning, the data is associated with numerous tasks, and we seek a model that may perform well on all tasks simultaneously, in pursuit of greater generalization. One challenge in meta-learning is how to exploit relationships between tasks and classes, which is overlooked by commonly used random or cyclic passes through data. In this work, we propose actively selecting samples on which to train by discerning covariates inside and between meta-training sets. Specifically, we cast the problem of selecting a sample from a number of meta-training sets as either a multi-armed bandit or a Markov Decision Process (MDP), depending on how one encapsulates correlation across tasks. We develop scheduling schemes based on Upper Confidence Bound (UCB), Gittins Index and tabular Markov Decision Problems (MDPs) solved with linear programming, where the reward is the scaled statistical accuracy to ensure it is a time-invariant function of state and action. Across a variety of experimental contexts, we observe significant reductions in sample complexity of active selection scheme relative to cyclic or i.i.d. sampling, demonstrating the merit of exploiting covariates in practice.

Data-driven fault classification is complicated by imbalanced training data and unknown fault classes. Fault diagnosis of dynamic systems is done by detecting changes in time-series data, for example residuals, caused by faults or system degradation. Different fault classes can result in similar residual outputs, especially for small faults which can be difficult to distinguish from nominal system operation. Analyzing how easy it is to distinguish data from different fault classes is crucial during the design process of a diagnosis system to evaluate if classification performance requirements can be met. Here, a data-driven model of different fault classes is used based on the Kullback-Leibler divergence. This is used to develop a framework for quantitative fault diagnosis performance analysis and open set fault classification. A data-driven fault classification algorithm is proposed which can handle unknown faults and also estimate the fault size using training data from known fault scenarios. To illustrate the usefulness of the proposed methods, data have been collected from an engine test bench to illustrate the design process of a data-driven diagnosis system, including quantitative fault diagnosis analysis and evaluation of the developed open set fault classification algorithm.

Model selection is a fundamental part of Bayesian statistical inference; a widely used tool in the field of epidemiology. Simple methods such as Akaike Information Criterion are commonly used but they do not incorporate the uncertainty of the model's parameters, which can give misleading choices when comparing models with similar fit to the data. One approach to model selection in a more rigorous way that uses the full posterior distributions of the models is to compute the ratio of the normalising constants (or model evidence), known as Bayes factors. These normalising constants integrate the posterior distribution over all parameters and balance over and under fitting. However, normalising constants often come in the form of intractable, high-dimensional integrals, therefore special probabilistic techniques need to be applied to correctly estimate the Bayes factors. One such method is thermodynamic integration (TI), which can be used to estimate the ratio of two models' evidence by integrating over a continuous path between the two un-normalised densities. In this paper we introduce a variation of the TI method, here referred to as referenced TI, which computes a single model's evidence in an efficient way by using a reference density such as a multivariate normal - where the normalising constant is known. We show that referenced TI, an asymptotically exact Monte Carlo method of calculating the normalising constant of a single model, in practice converges to the correct result much faster than other competing approaches such as the method of power posteriors. We illustrate the implementation of the algorithm on informative 1- and 2-dimensional examples, and apply it to a popular linear regression problem, and use it to select parameters for a model of the COVID-19 epidemic in South Korea.

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without systematically quantifying corresponding uncertainties. In this paper a novel approach towards fully Bayesian NNs is proposed, where training and predictions of a perceptron are performed within the Bayesian inference framework in closed-form. The weights and the predictions of the perceptron are considered Gaussian random variables. Analytical expressions for predicting the perceptron's output and for learning the weights are provided for commonly used activation functions like sigmoid or ReLU. This approach requires no computationally expensive gradient calculations and further allows sequential learning.