arXiv subjects

Santu Rana

Publications and source records attributed to Santu Rana.

At least 73 records · Page 4Linked to original sources

arXiv2020

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.

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arXiv2020

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.

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arXiv2020

Sparse Spectrum Gaussian Process for Bayesian Optimization

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this particular form of sparse approximations generates an overconfident GP, i.e. it produces less epistemic uncertainty than the original GP. Since the balance between predictive mean and the predictive variance is the key determinant to the success of Bayesian optimization, the current sparse spectrum methods are less suitable for it. We derive a new regularized marginal likelihood for finding the optimal frequencies to fix this over-confidence issue, particularly for Bayesian optimization. The regularizer trades off the accuracy in the model fitting with a targeted increase in the predictive variance of the resultant GP. Specifically, we use the entropy of the global maximum distribution from the posterior GP as the regularizer that needs to be maximized. Since this distribution cannot be calculated analytically, we first propose a Thompson sampling based approach and then a more efficient sequential Monte Carlo based approach to estimate it. Later, we also show that the Expected Improvement acquisition function can be used as a proxy for the maximum distribution, thus making the whole process further efficient. Experiments show considerable improvement to Bayesian optimization convergence rate over the vanilla sparse spectrum method and over a full GP when its covariance matrix is ill-conditioned due to the presence of a large number of observations.

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arXiv2020

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.

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arXiv2020

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.

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arXiv2020

Incorporating Expert Prior Knowledge into Experimental Design via Posterior Sampling

Scientific experiments are usually expensive due to complex experimental preparation and processing. Experimental design is therefore involved with the task of finding the optimal experimental input that results in the desirable output by using as few experiments as possible. Experimenters can often acquire the knowledge about the location of the global optimum. However, they do not know how to exploit this knowledge to accelerate experimental design. In this paper, we adopt the technique of Bayesian optimization for experimental design since Bayesian optimization has established itself as an efficient tool for optimizing expensive black-box functions. Again, it is unknown how to incorporate the expert prior knowledge about the global optimum into Bayesian optimization process. To address it, we represent the expert knowledge about the global optimum via placing a prior distribution on it and we then derive its posterior distribution. An efficient Bayesian optimization approach has been proposed via posterior sampling on the posterior distribution of the global optimum. We theoretically analyze the convergence of the proposed algorithm and discuss the robustness of incorporating expert prior. We evaluate the efficiency of our algorithm by optimizing synthetic functions and tuning hyperparameters of classifiers along with a real-world experiment on the synthesis of short polymer fiber. The results clearly demonstrate the advantages of our proposed method.

stat.ML↗

arXiv2020

Bayesian functional optimisation with shape prior

Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.

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arXiv2020

Accelerated Bayesian Optimization throughWeight-Prior Tuning

Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the objective as a linear function in a feature space implied by the given covariance K, with an arbitrary Gaussian weight prior ${\bf w} \sim \mathcal{N} ({\bf 0}, {\bf I})$. In many practical applications there is data available that has a similar (covariance) structure to the objective, but which, having different form, cannot be used directly in standard transfer learning. In this paper we show how such auxiliary data may be used to construct a GP covariance corresponding to a more appropriate weight prior for the objective function. Building on this, we show that we may accelerate BO by modeling the objective function using this (learned) weight prior, which we demonstrate on both test functions and a practical application to short-polymer fibre manufacture.

stat.ML↗

arXiv2020

Distributionally Robust Bayesian Quadrature Optimization

Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. Though Monte Carlo estimate is unbiased, it has high variance given a small set of samples; thus can result in a spurious objective function. We adopt the distributionally robust optimization perspective to this problem by maximizing the expected objective under the most adversarial distribution. In particular, we propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose. We demonstrate the empirical effectiveness of our proposed framework in synthetic and real-world problems, and characterize its theoretical convergence via Bayesian regret.

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arXiv2019

Bayesian Optimization for Categorical and Category-Specific Continuous Inputs

Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that formulates the problem as a multi-armed bandit problem, wherein each category corresponds to an arm with its reward distribution centered around the optimum of the objective function in continuous variables. Our goal is to identify the best arm and the maximizer of the corresponding continuous function simultaneously. Our algorithm uses a Thompson sampling scheme that helps connecting both multi-arm bandit and BO in a unified framework. We extend our method to batch BO to allow parallel optimization when multiple resources are available. We theoretically analyze our method for convergence and prove sub-linear regret bounds. We perform a variety of experiments: optimization of several benchmark functions, hyper-parameter tuning of a neural network, and automatic selection of the best machine learning model along with its optimal hyper-parameters (a.k.a automated machine learning). Comparisons with other methods demonstrate the effectiveness of our proposed method.

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arXiv2019

Multi-objective Bayesian optimisation with preferences over objectives

We present a multi-objective Bayesian 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". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm selects 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 is weighted by the probability of a point satisfying the constraints from a gradient Gaussian Process model. We demonstrate our algorithm on both synthetic and real-world problems.

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arXiv2019

Bayesian Optimization with Unknown Search Space

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.

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arXiv2019

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.

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arXiv2019

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'.

stat.ML↗

arXiv2019

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.

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arXiv2019

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.

cs.LG↗

arXiv2018

Practical Batch Bayesian Optimization for Less Expensive Functions

Bayesian optimization (BO) and its batch extensions are successful for optimizing expensive black-box functions. However, these traditional BO approaches are not yet ideal for optimizing less expensive functions when the computational cost of BO can dominate the cost of evaluating the blackbox function. Examples of these less expensive functions are cheap machine learning models, inexpensive physical experiment through simulators, and acquisition function optimization in Bayesian optimization. In this paper, we consider a batch BO setting for situations where function evaluations are less expensive. Our model is based on a new exploration strategy using geometric distance that provides an alternative way for exploration, selecting a point far from the observed locations. Using that intuition, we propose to use Sobol sequence to guide exploration that will get rid of running multiple global optimization steps as used in previous works. Based on the proposed distance exploration, we present an efficient batch BO approach. We demonstrate that our approach outperforms other baselines and global optimization methods when the function evaluations are less expensive.

cs.LG↗

arXiv2018

Hybrid Generative-Discriminative Models for Inverse Materials Design

Discovering new physical products and processes often demands enormous experimentation and expensive simulation. To design a new product with certain target characteristics, an extensive search is performed in the design space by trying out a large number of design combinations before reaching to the target characteristics. However, forward searching for the target design becomes prohibitive when the target is itself moving or only partially understood. To address this bottleneck, we propose to use backward prediction by leveraging the rich data generated during earlier exploration and construct a machine learning framework to predict the design parameters for any target in a single step. This poses two technical challenges: the first caused due to one-to-many mapping when learning the inverse problem and the second caused due to an user specifying the target specifications only partially. To overcome the challenges, we formulate this problem as conditional density estimation under high-dimensional setting with incomplete input and multimodal output. We solve the problem through a deep hybrid generative-discriminative model, which is trained end-to-end to predict the optimum design.

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