Cost-aware Multi-objective Bayesian optimisation

The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the ordering of dimensions of the search space based on the user's prior knowledge about their cost of usage. We formulate a new multi-objective Bayesian optimisation acquisition function with detailed analysis of the convergence that incorporates this cost-aware constraints while optimising the objective functions. We demonstrate our algorithm based on synthetic and real-world problems in hyperparameter tuning of neural networks and random forests.

Accelerating Experimental Design by Incorporating Experimenter Hunches

Experimental design is a process of obtaining a product with target property via experimentation. Bayesian optimization offers a sample-efficient tool for experimental design when experiments are expensive. Often, expert experimenters have 'hunches' about the behavior of the experimental system, offering potentials to further improve the efficiency. In this paper, we consider per-variable monotonic trend in the underlying property that results in a unimodal trend in those variables for a target value optimization. For example, sweetness of a candy is monotonic to the sugar content. However, to obtain a target sweetness, the utility of the sugar content becomes a unimodal function, which peaks at the value giving the target sweetness and falls off both ways. In this paper, we propose a novel method to solve such problems that achieves two main objectives: a) the monotonicity information is used to the fullest extent possible, whilst ensuring that b) the convergence guarantee remains intact. This is achieved by a two-stage Gaussian process modeling, where the first stage uses the monotonicity trend to model the underlying property, and the second stage uses `virtual' samples, sampled from the first, to model the target value optimization function. The process is made theoretically consistent by adding appropriate adjustment factor in the posterior computation, necessitated because of using the `virtual' samples. The proposed method is evaluated through both simulations and real world experimental design problems of a) new short polymer fiber with the target length, and b) designing of a new three dimensional porous scaffolding with a target porosity. In all scenarios our method demonstrates faster convergence than the basic Bayesian optimization approach not using such `hunches'.

Learning to Reason with Relational Video Representation for Question Answering

How does machine learn to reason about the content of a video in answering a question? A Video QA system must simultaneously understand language, represent visual content over space-time, and iteratively transform these representations in response to lingual content in the query, and finally arriving at a sensible answer. While recent advances in textual and visual question answering have come up with sophisticated visual representation and neural reasoning mechanisms, major challenges in Video QA remain on dynamic grounding of concepts, relations and actions to support the reasoning process. We present a new end-to-end layered architecture for Video QA, which is composed of a question-guided video representation layer and a generic reasoning layer to produce answer. The video is represented using a hierarchical model that encodes visual information about objects, actions and relations in space-time given the textual cues from the question. The encoded representation is then passed to a reasoning module, which in this paper, is implemented as a MAC net. The system is evaluated on the SVQA (synthetic) and TGIF-QA datasets (real), demonstrating state-of-the-art results, with a large margin in the case of multi-step reasoning.

Sparse Spectrum Gaussian Process for Bayesian Optimisation

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimisation. Whilst the current sparse spectrum methods provide good approximations for regression problems, it is observed that this particular form of sparse approximations generates an overconfident GP, i.e. it predicts less variance than the original GP. Since the balance between predictive mean and the predictive variance is a key determinant in the success of Bayesian optimisation, the current sparse spectrum methods are less suitable. We derive a regularised marginal likelihood for finding the optimal frequencies in optimisation problems. The regulariser trades the accuracy in the model fitting with the targeted increase in the variance of the resultant GP. We first consider the entropy of the distribution over the maxima as the regulariser that needs to be maximised. Later we show that the Expected Improvement acquisition function can also be used as a proxy for that, thus making the optimisation less computationally expensive. Experiments show an increase in the Bayesian optimisation convergence rate over the vanilla sparse spectrum method.

Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection

Deep autoencoder has been extensively used for anomaly detection. Training on the normal data, the autoencoder is expected to produce higher reconstruction error for the abnormal inputs than the normal ones, which is adopted as a criterion for identifying anomalies. However, this assumption does not always hold in practice. It has been observed that sometimes the autoencoder "generalizes" so well that it can also reconstruct anomalies well, leading to the miss detection of anomalies. To mitigate this drawback for autoencoder based anomaly detector, we propose to augment the autoencoder with a memory module and develop an improved autoencoder called memory-augmented autoencoder, i.e. MemAE. Given an input, MemAE firstly obtains the encoding from the encoder and then uses it as a query to retrieve the most relevant memory items for reconstruction. At the training stage, the memory contents are updated and are encouraged to represent the prototypical elements of the normal data. At the test stage, the learned memory will be fixed, and the reconstruction is obtained from a few selected memory records of the normal data. The reconstruction will thus tend to be close to a normal sample. Thus the reconstructed errors on anomalies will be strengthened for anomaly detection. MemAE is free of assumptions on the data type and thus general to be applied to different tasks. Experiments on various datasets prove the excellent generalization and high effectiveness of the proposed MemAE.

Learning Regularity in Skeleton Trajectories for Anomaly Detection in Videos

Appearance features have been widely used in video anomaly detection even though they contain complex entangled factors. We propose a new method to model the normal patterns of human movements in surveillance video for anomaly detection using dynamic skeleton features. We decompose the skeletal movements into two sub-components: global body movement and local body posture. We model the dynamics and interaction of the coupled features in our novel Message-Passing Encoder-Decoder Recurrent Network. We observed that the decoupled features collaboratively interact in our spatio-temporal model to accurately identify human-related irregular events from surveillance video sequences. Compared to traditional appearance-based models, our method achieves superior outlier detection performance. Our model also offers "open-box" examination and decision explanation made possible by the semantically understandable features and a network architecture supporting interpretability.

Stable Bayesian Optimisation via Direct Stability Quantification

In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multiple gradient Gaussian Process models to estimate the probability that worst-case output variation for specified input perturbation exceeded the desired maxima, and these probabilities are then used to (a) guide the optimisation process toward solutions satisfying our stability criteria and (b) post-filter results to find the best stable solution. We exhibit our algorithm on synthetic and real-world problems and demonstrate that it is able to effectively find stable maxima.

Multi-objective Bayesian optimisation with preferences over objectives

We present a Bayesian multi-objective optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type `objective A is more important than objective B'. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm searches for and returns only those Pareto-optimal points that satisfy these constraints. We formulate a new acquisition function based on expected improvement in dominated hypervolume (EHI) to ensure that the subset of Pareto front satisfying the constraints is thoroughly explored. The hypervolume calculation only includes those points that satisfy the preference-order constraints, where the probability of a point satisfying the constraints is calculated from a gradient Gaussian Process model. We demonstrate our algorithm on both synthetic and real-world problems.

Improving Generalization and Stability of Generative Adversarial Networks

Generative Adversarial Networks (GANs) are one of the most popular tools for learning complex high dimensional distributions. However, generalization properties of GANs have not been well understood. In this paper, we analyze the generalization of GANs in practical settings. We show that discriminators trained on discrete datasets with the original GAN loss have poor generalization capability and do not approximate the theoretically optimal discriminator. We propose a zero-centered gradient penalty for improving the generalization of the discriminator by pushing it toward the optimal discriminator. The penalty guarantees the generalization and convergence of GANs. Experiments on synthetic and large scale datasets verify our theoretical analysis.

Fast Hyperparameter Tuning using Bayesian Optimization with Directional Derivatives

In this paper we develop a Bayesian optimization based hyperparameter tuning framework inspired by statistical learning theory for classifiers. We utilize two key facts from PAC learning theory; the generalization bound will be higher for a small subset of data compared to the whole, and the highest accuracy for a small subset of data can be achieved with a simple model. We initially tune the hyperparameters on a small subset of training data using Bayesian optimization. While tuning the hyperparameters on the whole training data, we leverage the insights from the learning theory to seek more complex models. We realize this by using directional derivative signs strategically placed in the hyperparameter search space to seek a more complex model than the one obtained with small data. We demonstrate the performance of our method on the tasks of tuning the hyperparameters of several machine learning algorithms.