Unsupervised Anomaly Detection on Temporal Multiway Data

Temporal anomaly detection looks for irregularities over space-time. Unsupervised temporal models employed thus far typically work on sequences of feature vectors, and much less on temporal multiway data. We focus our investigation on two-way data, in which a data matrix is observed at each time step. Leveraging recent advances in matrix-native recurrent neural networks, we investigated strategies for data arrangement and unsupervised training for temporal multiway anomaly detection. These include compressing-decompressing, encoding-predicting, and temporal data differencing. We conducted a comprehensive suite of experiments to evaluate model behaviors under various settings on synthetic data, moving digits, and ECG recordings. We found interesting phenomena not previously reported. These include the capacity of the compact matrix LSTM to compress noisy data near perfectly, making the strategy of compressing-decompressing data ill-suited for anomaly detection under the noise. Also, long sequence of vectors can be addressed directly by matrix models that allow very long context and multiple step prediction. Overall, the encoding-predicting strategy works very well for the matrix LSTMs in the conducted experiments, thanks to its compactness and better fit to the data dynamics.

Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

Sequential Subspace Search for Functional Bayesian Optimization Incorporating Experimenter Intuition

We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity etc.) of the optimal solution encoded into the covariance function of a Gaussian Process. Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting point (origin) for the next subspace. Using the concept of effective dimensionality, we analyse the convergence of our algorithm and provide a regret bound to show that our algorithm converges in sub-linear time provided a finite effective dimension exists. We test our algorithm in simulated and real-world experiments, namely blind function matching, finding the optimal precipitation-strengthening function for an aluminium alloy, and learning rate schedule optimisation for deep networks.

Bayesian Optimization with Missing Inputs

Bayesian optimization (BO) is an efficient method for optimizing expensive black-box functions. In real-world applications, BO often faces a major problem of missing values in inputs. The missing inputs can happen in two cases. First, the historical data for training BO often contain missing values. Second, when performing the function evaluation (e.g. computing alloy strength in a heat treatment process), errors may occur (e.g. a thermostat stops working) leading to an erroneous situation where the function is computed at a random unknown value instead of the suggested value. To deal with this problem, a common approach just simply skips data points where missing values happen. Clearly, this naive method cannot utilize data efficiently and often leads to poor performance. In this paper, we propose a novel BO method to handle missing inputs. We first find a probability distribution of each missing value so that we can impute the missing value by drawing a sample from its distribution. We then develop a new acquisition function based on the well-known Upper Confidence Bound (UCB) acquisition function, which considers the uncertainty of imputed values when suggesting the next point for function evaluation. We conduct comprehensive experiments on both synthetic and real-world applications to show the usefulness of our method.

DeepCoDA: personalized interpretability for compositional health data

Interpretability allows the domain-expert to directly evaluate the model's relevance and reliability, a practice that offers assurance and builds trust. In the healthcare setting, interpretable models should implicate relevant biological mechanisms independent of technical factors like data pre-processing. We define personalized interpretability as a measure of sample-specific feature attribution, and view it as a minimum requirement for a precision health model to justify its conclusions. Some health data, especially those generated by high-throughput sequencing experiments, have nuances that compromise precision health models and their interpretation. These data are compositional, meaning that each feature is conditionally dependent on all other features. We propose the Deep Compositional Data Analysis (DeepCoDA) framework to extend precision health modelling to high-dimensional compositional data, and to provide personalized interpretability through patient-specific weights. Our architecture maintains state-of-the-art performance across 25 real-world data sets, all while producing interpretations that are both personalized and fully coherent for compositional data.

Scalable Backdoor Detection in Neural Networks

Recently, it has been shown that deep learning models are vulnerable to Trojan attacks, where an attacker can install a backdoor during training time to make the resultant model misidentify samples contaminated with a small trigger patch. Current backdoor detection methods fail to achieve good detection performance and are computationally expensive. In this paper, we propose a novel trigger reverse-engineering based approach whose computational complexity does not scale with the number of labels, and is based on a measure that is both interpretable and universal across different network and patch types. In experiments, we observe that our method achieves a perfect score in separating Trojaned models from pure models, which is an improvement over the current state-of-the art method.

Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation

In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret. We also provide results showing that our method achieves better performance than GP-UCB in a range of real-world and synthetic problems.

DeepCoDA: personalized interpretability for compositional health

Interpretability allows the domain-expert to directly evaluate the model's relevance and reliability, a practice that offers assurance and builds trust. In the healthcare setting, interpretable models should implicate relevant biological mechanisms independent of technical factors like data pre-processing. We define personalized interpretability as a measure of sample-specific feature attribution, and view it as a minimum requirement for a precision health model to justify its conclusions. Some health data, especially those generated by high-throughput sequencing experiments, have nuances that compromise precision health models and their interpretation. These data are compositional, meaning that each feature is conditionally dependent on all other features. We propose the DeepCoDA framework to extend precision health modelling to high-dimensional compositional data, and to provide personalized interpretability through patient-specific weights. Our architecture maintains state-of-the-art performance across 25 real-world data sets, all while producing interpretations that are both personalized and fully coherent for compositional data.

HyperVAE: A Minimum Description Length Variational Hyper-Encoding Network

We propose a framework called HyperVAE for encoding distributions of distributions. When a target distribution is modeled by a VAE, its neural network parameters \theta is drawn from a distribution p(\theta) which is modeled by a hyper-level VAE. We propose a variational inference using Gaussian mixture models to implicitly encode the parameters \theta into a low dimensional Gaussian distribution. Given a target distribution, we predict the posterior distribution of the latent code, then use a matrix-network decoder to generate a posterior distribution q(\theta). HyperVAE can encode the parameters \theta in full in contrast to common hyper-networks practices, which generate only the scale and bias vectors as target-network parameters. Thus HyperVAE preserves much more information about the model for each task in the latent space. We discuss HyperVAE using the minimum description length (MDL) principle and show that it helps HyperVAE to generalize. We evaluate HyperVAE in density estimation tasks, outlier detection and discovery of novel design classes, demonstrating its efficacy.

Incorporating Expert Prior in Bayesian Optimisation via Space Warping

Bayesian optimisation is a well-known sample-efficient method for the optimisation of expensive black-box functions. However when dealing with big search spaces the algorithm goes through several low function value regions before reaching the optimum of the function. Since the function evaluations are expensive in terms of both money and time, it may be desirable to alleviate this problem. One approach to subside this cold start phase is to use prior knowledge that can accelerate the optimisation. In its standard form, Bayesian optimisation assumes the likelihood of any point in the search space being the optimum is equal. Therefore any prior knowledge that can provide information about the optimum of the function would elevate the optimisation performance. In this paper, we represent the prior knowledge about the function optimum through a prior distribution. The prior distribution is then used to warp the search space in such a way that space gets expanded around the high probability region of function optimum and shrinks around low probability region of optimum. We incorporate this prior directly in function model (Gaussian process), by redefining the kernel matrix, which allows this method to work with any acquisition function, i.e. acquisition agnostic approach. We show the superiority of our method over standard Bayesian optimisation method through optimisation of several benchmark functions and hyperparameter tuning of two algorithms: Support Vector Machine (SVM) and Random forest.