arXiv subjects

Svetha Venkatesh

Publications and source records attributed to Svetha Venkatesh.

At least 91 records · Page 5Linked to original sources

arXiv2020

High Dimensional Level Set Estimation with Bayesian Neural Network

Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods do not work well with high dimensional inputs. This paper proposes novel methods to solve the high dimensional LSE problems using Bayesian Neural Networks. In particular, we consider two types of LSE problems: (1) \textit{explicit} LSE problem where the threshold level is a fixed user-specified value, and, (2) \textit{implicit} LSE problem where the threshold level is defined as a percentage of the (unknown) maximum of the objective function. For each problem, we derive the corresponding theoretic information based acquisition function to sample the data points so as to maximally increase the level set accuracy. Furthermore, we also analyse the theoretical time complexity of our proposed acquisition functions, and suggest a practical methodology to efficiently tune the network hyper-parameters to achieve high model accuracy. Numerical experiments on both synthetic and real-world datasets show that our proposed method can achieve better results compared to existing state-of-the-art approaches.

stat.ML↗

arXiv2020

Distributional Reinforcement Learning via Moment Matching

We consider the problem of learning a set of probability distributions from the empirical Bellman dynamics in distributional reinforcement learning (RL), a class of state-of-the-art methods that estimate the distribution, as opposed to only the expectation, of the total return. We formulate a method that learns a finite set of statistics from each return distribution via neural networks, as in (Bellemare, Dabney, and Munos 2017; Dabney et al. 2018b). Existing distributional RL methods however constrain the learned statistics to \emph{predefined} functional forms of the return distribution which is both restrictive in representation and difficult in maintaining the predefined statistics. Instead, we learn \emph{unrestricted} statistics, i.e., deterministic (pseudo-)samples, of the return distribution by leveraging a technique from hypothesis testing known as maximum mean discrepancy (MMD), which leads to a simpler objective amenable to backpropagation. Our method can be interpreted as implicitly matching all orders of moments between a return distribution and its Bellman target. We establish sufficient conditions for the contraction of the distributional Bellman operator and provide finite-sample analysis for the deterministic samples in distribution approximation. Experiments on the suite of Atari games show that our method outperforms the standard distributional RL baselines and sets a new record in the Atari games for non-distributed agents.

cs.LG↗

arXiv2020

Logically Consistent Loss for Visual Question Answering

Given an image, a back-ground knowledge, and a set of questions about an object, human learners answer the questions very consistently regardless of question forms and semantic tasks. The current advancement in neural-network based Visual Question Answering (VQA), despite their impressive performance, cannot ensure such consistency due to identically distribution (i.i.d.) assumption. We propose a new model-agnostic logic constraint to tackle this issue by formulating a logically consistent loss in the multi-task learning framework as well as a data organisation called family-batch and hybrid-batch. To demonstrate usefulness of this proposal, we train and evaluate MAC-net based VQA machines with and without the proposed logically consistent loss and the proposed data organization. The experiments confirm that the proposed loss formulae and introduction of hybrid-batch leads to more consistency as well as better performance. Though the proposed approach is tested with MAC-net, it can be utilised in any other QA methods whenever the logical consistency between answers exist.

cs.CV↗

arXiv2020

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.

stat.ML↗

arXiv2020

Neurocoder: Learning General-Purpose Computation Using Stored Neural Programs

Artificial Neural Networks are uniquely adroit at machine learning by processing data through a network of artificial neurons. The inter-neuronal connection weights represent the learnt Neural Program that instructs the network on how to compute the data. However, without an external memory to store Neural Programs, they are restricted to only one, overwriting learnt programs when trained on new data. This is functionally equivalent to a special-purpose computer. Here we design Neurocoder, an entirely new class of general-purpose conditional computational machines in which the neural network "codes" itself in a data-responsive way by composing relevant programs from a set of shareable, modular programs. This can be considered analogous to building Lego structures from simple Lego bricks. Notably, our bricks change their shape through learning. External memory is used to create, store and retrieve modular programs. Like today's stored-program computers, Neurocoder can now access diverse programs to process different data. Unlike manually crafted computer programs, Neurocoder creates programs through training. Integrating Neurocoder into current neural architectures, we demonstrate new capacity to learn modular programs, handle severe pattern shifts and remember old programs as new ones are learnt, and show substantial performance improvement in solving object recognition, playing video games and continual learning tasks. Such integration with Neurocoder increases the computation capability of any current neural network and endows it with entirely new capacity to reuse simple programs to build complex ones. For the first time a Neural Program is treated as a datum in memory, paving the ways for modular, recursive and procedural neural programming.

cs.LG↗

arXiv2020

Theory of Mind with Guilt Aversion Facilitates Cooperative Reinforcement Learning

Guilt aversion induces experience of a utility loss in people if they believe they have disappointed others, and this promotes cooperative behaviour in human. In psychological game theory, guilt aversion necessitates modelling of agents that have theory about what other agents think, also known as Theory of Mind (ToM). We aim to build a new kind of affective reinforcement learning agents, called Theory of Mind Agents with Guilt Aversion (ToMAGA), which are equipped with an ability to think about the wellbeing of others instead of just self-interest. To validate the agent design, we use a general-sum game known as Stag Hunt as a test bed. As standard reinforcement learning agents could learn suboptimal policies in social dilemmas like Stag Hunt, we propose to use belief-based guilt aversion as a reward shaping mechanism. We show that our belief-based guilt averse agents can efficiently learn cooperative behaviours in Stag Hunt Games.

cs.AI↗

arXiv2020

Learning Transferable Domain Priors for Safe Exploration in Reinforcement Learning

Prior access to domain knowledge could significantly improve the performance of a reinforcement learning agent. In particular, it could help agents avoid potentially catastrophic exploratory actions, which would otherwise have to be experienced during learning. In this work, we identify consistently undesirable actions in a set of previously learned tasks, and use pseudo-rewards associated with them to learn a prior policy. In addition to enabling safer exploratory behaviors in subsequent tasks in the domain, we show that these priors are transferable to similar environments, and can be learned off-policy and in parallel with the learning of other tasks in the domain. We compare our approach to established, state-of-the-art algorithms in both discrete as well as continuous environments, and demonstrate that it exhibits a safer exploratory behavior while learning to perform arbitrary tasks in the domain. We also present a theoretical analysis to support these results, and briefly discuss the implications and some alternative formulations of this approach, which could also be useful in certain scenarios.

cs.AI↗

arXiv2020

From deep to Shallow: Equivalent Forms of Deep Networks in Reproducing Kernel Krein Space and Indefinite Support Vector Machines

In this paper we explore a connection between deep networks and learning in reproducing kernel Krein space. Our approach is based on the concept of push-forward - that is, taking a fixed non-linear transform on a linear projection and converting it to a linear projection on the output of a fixed non-linear transform, pushing the weights forward through the non-linearity. Applying this repeatedly from the input to the output of a deep network, the weights can be progressively "pushed" to the output layer, resulting in a flat network that has the form of a fixed non-linear map (whose form is determined by the structure of the deep network) followed by a linear projection determined by the weight matrices - that is, we take a deep network and convert it to an equivalent (indefinite) kernel machine. We then investigate the implications of this transformation for capacity control and uniform convergence, and provide a Rademacher complexity bound on the deep network in terms of Rademacher complexity in reproducing kernel Krein space. Finally, we analyse the sparsity properties of the flat representation, showing that the flat weights are (effectively) Lp-"norm" regularised with 0<p<1 (bridge regression).

stat.ML↗

arXiv2020

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.

cs.LG↗

arXiv2020

Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization

Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find global maximisation of acquisition function, which itself is a non-convex optimization problem in the original search space. With growing dimensions, the computational budget for this maximisation gets increasingly short leading to inaccurate solution of the maximisation. This inaccuracy adversely affects both the convergence and the efficiency of BO. We propose a novel approach where the acquisition function only requires maximisation on a discrete set of low dimensional subspaces embedded in the original high-dimensional search space. Our method is free of any low dimensional structure assumption on the function unlike many recent high-dimensional BO methods. Optimising acquisition function in low dimensional subspaces allows our method to obtain accurate solutions within limited computational budget. We show that in spite of this convenience, our algorithm remains convergent. In particular, cumulative regret of our algorithm only grows sub-linearly with the number of iterations. More importantly, as evident from our regret bounds, our algorithm provides a way to trade the convergence rate with the number of subspaces used in the optimisation. Finally, when the number of subspaces is "sufficiently large", our algorithm's cumulative regret is at most $\mathcal{O}^{*}(\sqrt{Tγ_T})$ as opposed to $\mathcal{O}^{*}(\sqrt{DTγ_T})$ for the GP-UCB of Srinivas et al. (2012), reducing a crucial factor $\sqrt{D}$ where $D$ being the dimensional number of input space.

stat.ML↗

arXiv2020

Learning to Abstract and Predict Human Actions

Human activities are naturally structured as hierarchies unrolled over time. For action prediction, temporal relations in event sequences are widely exploited by current methods while their semantic coherence across different levels of abstraction has not been well explored. In this work we model the hierarchical structure of human activities in videos and demonstrate the power of such structure in action prediction. We propose Hierarchical Encoder-Refresher-Anticipator, a multi-level neural machine that can learn the structure of human activities by observing a partial hierarchy of events and roll-out such structure into a future prediction in multiple levels of abstraction. We also introduce a new coarse-to-fine action annotation on the Breakfast Actions videos to create a comprehensive, consistent, and cleanly structured video hierarchical activity dataset. Through our experiments, we examine and rethink the settings and metrics of activity prediction tasks toward unbiased evaluation of prediction systems, and demonstrate the role of hierarchical modeling toward reliable and detailed long-term action forecasting.

cs.CV↗

arXiv2020

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.

cs.LG↗

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.

cs.LG↗

arXiv2020

Self-Attentive Associative Memory

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experiences (item memory) and their occurring relationships (relational memory). The idea is implemented through a novel Self-attentive Associative Memory (SAM) operator. Found upon outer product, SAM forms a set of associative memories that represent the hypothetical high-order relationships between arbitrary pairs of memory elements, through which a relational memory is constructed from an item memory. The two memories are wired into a single sequential model capable of both memorization and relational reasoning. We achieve competitive results with our proposed two-memory model in a diversity of machine learning tasks, from challenging synthetic problems to practical testbeds such as geometry, graph, reinforcement learning, and question answering.

cs.LG↗

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.

cs.CV↗

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.

cs.LG↗

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.

cs.LG↗

arXiv2020

Neural Reasoning, Fast and Slow, for Video Question Answering

What does it take to design a machine that learns to answer natural questions about a video? 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 lingual and visual question answering have enabled sophisticated representations and neural reasoning mechanisms, major challenges in Video QA remain on dynamic grounding of concepts, relations and actions to support the reasoning process. Inspired by the dual-process account of human reasoning, we design a dual process neural architecture, which is composed of a question-guided video processing module (System 1, fast and reactive) followed by a generic reasoning module (System 2, slow and deliberative). System 1 is a hierarchical model that encodes visual patterns about objects, actions and relations in space-time given the textual cues from the question. The encoded representation is a set of high-level visual features, which are then passed to System 2. Here multi-step inference follows to iteratively chain visual elements as instructed by the textual elements. The system is evaluated on the SVQA (synthetic) and TGIF-QA datasets (real), demonstrating competitive results, with a large margin in the case of multi-step reasoning.

cs.CV↗