Gavin Brown

Ben Jacobsen, Tomas Gonzales, Gavin Brown et al.

E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels.

Gavin Brown, Ephraim Linder, Mahbod Majid et al.

We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a classical paradigm that partitions the dataset into blocks, estimates the statistic on each block, and then privately aggregates the estimates.While practical and generically applicable, this approach is quite data-hungry. We improve upon this framework for the class of monotone statistics -- compared to subsample-and-aggregate, our algorithms save a factor of $t$ in sample complexity and pay a factor of $e^t$ in running time, where $t>0$ is a tunable parameter. We complement our results with a query-complexity lower bound, showing that our algorithms are essentially optimal for this task. As an application, we obtain improved results for private eigenvalue estimation, private loss estimation, and privately estimating a single parameter of a high-dimensional model, e.g., in linear regression.

Gavin Brown, Samuel B. Hopkins, Adam Smith

We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$ samples from a (sub-)Gaussian distribution with unknown mean $μ$ and covariance $Σ$, our $(\varepsilon,δ)$-differentially private estimator produces $\tildeμ$ such that $\|μ- \tildeμ\|_Σ \leq α$ as long as $n \gtrsim \tfrac d {α^2} + \tfrac{d \sqrt{\log 1/δ}}{α\varepsilon}+\frac{d\log 1/δ}{\varepsilon}$. The Mahalanobis error metric $\|μ- \hatμ\|_Σ$ measures the distance between $\hat μ$ and $μ$ relative to $Σ$; it characterizes the error of the sample mean. Our algorithm runs in time $\tilde{O}(nd^{ω- 1} + nd/\varepsilon)$, where $ω< 2.38$ is the matrix multiplication exponent. We adapt an exponential-time approach of Brown, Gaboardi, Smith, Ullman, and Zakynthinou (2021), giving efficient variants of stable mean and covariance estimation subroutines that also improve the sample complexity to the nearly optimal bound above. Our stable covariance estimator can be turned to private covariance estimation for unrestricted subgaussian distributions. With $n\gtrsim d^{3/2}$ samples, our estimate is accurate in spectral norm. This is the first such algorithm using $n= o(d^2)$ samples, answering an open question posed by Alabi et al. (2022). With $n\gtrsim d^2$ samples, our estimate is accurate in Frobenius norm. This leads to a fast, nearly optimal algorithm for private learning of unrestricted Gaussian distributions in TV distance. Duchi, Haque, and Kuditipudi (2023) obtained similar results independently and concurrently.

Danny Wood, Tingting Mu, Andrew Webb et al.

We present a theory of ensemble diversity, explaining the nature of diversity for a wide range of supervised learning scenarios. This challenge has been referred to as the holy grail of ensemble learning, an open research issue for over 30 years. Our framework reveals that diversity is in fact a hidden dimension in the bias-variance decomposition of the ensemble loss. We prove a family of exact bias-variance-diversity decompositions, for a wide range of losses in both regression and classification, e.g., squared, cross-entropy, and Poisson losses. For losses where an additive bias-variance decomposition is not available (e.g., 0/1 loss) we present an alternative approach: quantifying the effects of diversity, which turn out to be dependent on the label distribution. Overall, we argue that diversity is a measure of model fit, in precisely the same sense as bias and variance, but accounting for statistical dependencies between ensemble members. Thus, we should not be maximising diversity as so many works aim to do -- instead, we have a bias/variance/diversity trade-off to manage.

Gavin Brown, Mark Bun, Adam Smith

We give lower bounds on the amount of memory required by one-pass streaming algorithms for solving several natural learning problems. In a setting where examples lie in $\{0,1\}^d$ and the optimal classifier can be encoded using $κ$ bits, we show that algorithms which learn using a near-minimal number of examples, $\tilde O(κ)$, must use $\tilde Ω( dκ)$ bits of space. Our space bounds match the dimension of the ambient space of the problem's natural parametrization, even when it is quadratic in the size of examples and the final classifier. For instance, in the setting of $d$-sparse linear classifiers over degree-2 polynomial features, for which $κ=Θ(d\log d)$, our space lower bound is $\tildeΩ(d^2)$. Our bounds degrade gracefully with the stream length $N$, generally having the form $\tildeΩ\left(dκ\cdot \fracκ{N}\right)$. Bounds of the form $Ω(dκ)$ were known for learning parity and other problems defined over finite fields. Bounds that apply in a narrow range of sample sizes are also known for linear regression. Ours are the first such bounds for problems of the type commonly seen in recent learning applications that apply for a large range of input sizes.

Danny Wood, Tingting Mu, Gavin Brown

We introduce a novel bias-variance decomposition for a range of strictly convex margin losses, including the logistic loss (minimized by the classic LogitBoost algorithm), as well as the squared margin loss and canonical boosting loss. Furthermore, we show that, for all strictly convex margin losses, the expected risk decomposes into the risk of a "central" model and a term quantifying variation in the functional margin with respect to variations in the training data. These decompositions provide a diagnostic tool for practitioners to understand model overfitting/underfitting, and have implications for additive ensemble models -- for example, when our bias-variance decomposition holds, there is a corresponding "ambiguity" decomposition, which can be used to quantify model diversity.

Konstantinos Iordanou, Timothy Atkinson, Emre Ozer et al.

A typical machine learning (ML) development cycle for edge computing is to maximise the performance during model training and then minimise the memory/area footprint of the trained model for deployment on edge devices targeting CPUs, GPUs, microcontrollers, or custom hardware accelerators. This paper proposes a methodology for automatically generating predictor circuits for classification of tabular data with comparable prediction performance to conventional ML techniques while using substantially fewer hardware resources and power. The proposed methodology uses an evolutionary algorithm to search over the space of logic gates and automatically generates a classifier circuit with maximised training prediction accuracy. Classifier circuits are so tiny (i.e., consisting of no more than 300 logic gates) that they are called "Tiny Classifier" circuits, and can efficiently be implemented in ASIC or on an FPGA. We empirically evaluate the automatic Tiny Classifier circuit generation methodology or "Auto Tiny Classifiers" on a wide range of tabular datasets, and compare it against conventional ML techniques such as Amazon's AutoGluon, Google's TabNet and a neural search over Multi-Layer Perceptrons. Despite Tiny Classifiers being constrained to a few hundred logic gates, we observe no statistically significant difference in prediction performance in comparison to the best-performing ML baseline. When synthesised as a Silicon chip, Tiny Classifiers use 8-18x less area and 4-8x less power. When implemented as an ultra-low cost chip on a flexible substrate (i.e., FlexIC), they occupy 10-75x less area and consume 13-75x less power compared to the most hardware-efficient ML baseline. On an FPGA, Tiny Classifiers consume 3-11x fewer resources.

Sara Summerton, Ann Tivey, Rohan Shotton et al.

In this work, we present a novel trajectory comparison algorithm to identify abnormal vital sign trends, with the aim of improving recognition of deteriorating health. There is growing interest in continuous wearable vital sign sensors for monitoring patients remotely at home. These monitors are usually coupled to an alerting system, which is triggered when vital sign measurements fall outside a predefined normal range. Trends in vital signs, such as increasing heart rate, are often indicative of deteriorating health, but are rarely incorporated into alerting systems. We introduce a dynamic time warp distance-based measure to compare time series trajectories. We split each multi-variable sign time series into 180 minute, non-overlapping epochs. We then calculate the distance between all pairs of epochs. Each epoch is characterized by its mean pairwise distance (average link distance) to all other epochs, with clusters forming with nearby epochs. We demonstrate in synthetically generated data that this method can identify abnormal epochs and cluster epochs with similar trajectories. We then apply this method to a real-world data set of vital signs from 8 patients who had recently been discharged from hospital after contracting COVID-19. We show how outlier epochs correspond well with the abnormal vital signs and identify patients who were subsequently readmitted to hospital.

Michele Filannino, Gavin Brown, Goran Nenadic

This paper describes a temporal expression identification and normalization system, ManTIME, developed for the TempEval-3 challenge. The identification phase combines the use of conditional random fields along with a post-processing identification pipeline, whereas the normalization phase is carried out using NorMA, an open-source rule-based temporal normalizer. We investigate the performance variation with respect to different feature types. Specifically, we show that the use of WordNet-based features in the identification task negatively affects the overall performance, and that there is no statistically significant difference in using gazetteers, shallow parsing and propositional noun phrases labels on top of the morphological features. On the test data, the best run achieved 0.95 (P), 0.85 (R) and 0.90 (F1) in the identification phase. Normalization accuracies are 0.84 (type attribute) and 0.77 (value attribute). Surprisingly, the use of the silver data (alone or in addition to the gold annotated ones) does not improve the performance.

Adam Perrett, Danny Wood, Gavin Brown

This work presents a novel algorithm for transforming a neural network into a spline representation. Unlike previous work that required convex and piecewise-affine network operators to create a max-affine spline alternate form, this work relaxes this constraint. The only constraint is that the function be bounded and possess a well-define second derivative, although this was shown experimentally to not be strictly necessary. It can also be performed over the whole network rather than on each layer independently. As in previous work, this bridges the gap between neural networks and approximation theory but also enables the visualisation of network feature maps. Mathematical proof and experimental investigation of the technique is performed with approximation error and feature maps being extracted from a range of architectures, including convolutional neural networks.

Robert Gieselmann, Henrike von Huelsen, Mihai Samson et al.

Generative models trained on synthetic plan data are a promising approach to generalized planning. Recent work has focused on finding any valid plan, rather than a high-quality solution. We address the challenge of producing high-quality plans, a computationally hard problem, in sub-exponential time. First, we demonstrate that, given optimal data, a decoder-only transformer can generate high-quality plans for unseen problem instances. Second, we show how to self-improve an initial model trained on sub-optimal data. Each round of self-improvement combines multiple model calls with graph search to generate improved plans, used for model fine-tuning. An experimental study on four domains: Blocksworld, Logistics, Labyrinth, and Sokoban, shows on average a 30% reduction in plan length over the source symbolic planner, with over 80% of plans being optimal, where the optimum is known. Plan quality is further improved by inference-time search. The model's latency scales sub-exponentially in contrast to the satisficing and optimal symbolic planners to which we compare. Together, these results suggest that self-improvement with generative models offers a scalable approach for high-quality plan generation.

Maryam Aliakbarpour, Konstantina Bairaktari, Gavin Brown et al.

Metalearning and multitask learning are two frameworks for solving a group of related learning tasks more efficiently than we could hope to solve each of the individual tasks on their own. In multitask learning, we are given a fixed set of related learning tasks and need to output one accurate model per task, whereas in metalearning we are given tasks that are drawn i.i.d. from a metadistribution and need to output some common information that can be easily specialized to new tasks from the metadistribution. We consider a binary classification setting where tasks are related by a shared representation, that is, every task $P$ can be solved by a classifier of the form $f_{P} \circ h$ where $h \in H$ is a map from features to a representation space that is shared across tasks, and $f_{P} \in F$ is a task-specific classifier from the representation space to labels. The main question we ask is how much data do we need to metalearn a good representation? Here, the amount of data is measured in terms of the number of tasks $t$ that we need to see and the number of samples $n$ per task. We focus on the regime where $n$ is extremely small. Our main result shows that, in a distribution-free setting where the feature vectors are in $\mathbb{R}^d$, the representation is a linear map from $\mathbb{R}^d \to \mathbb{R}^k$, and the task-specific classifiers are halfspaces in $\mathbb{R}^k$, we can metalearn a representation with error $\varepsilon$ using $n = k+2$ samples per task, and $d \cdot (1/\varepsilon)^{O(k)}$ tasks. Learning with so few samples per task is remarkable because metalearning would be impossible with $k+1$ samples per task, and because we cannot even hope to learn an accurate task-specific classifier with $k+2$ samples per task. Our work also yields a characterization of distribution-free multitask learning and reductions between meta and multitask learning.

Gavin Brown, Krishnamurthy Dvijotham, Georgina Evans et al.

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time step. Our analysis leads to new results on the algorithm's accuracy: for a proper fixed choice of hyperparameters, the sample complexity depends only linearly on the dimension of the data. This matches the dimension-dependence of the (non-private) ordinary least squares estimator as well as that of recent private algorithms that rely on sophisticated adaptive gradient-clipping schemes (Varshney et al., 2022; Liu et al., 2023). Our analysis of the iterates' distribution also allows us to construct confidence intervals for the empirical optimizer which adapt automatically to the variance of the algorithm on a particular data set. We validate our theorems through experiments on synthetic data.

Gavin Brown, Jonathan Hayase, Samuel Hopkins et al.

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix. All prior private algorithms for this task require either $d^{3/2}$ examples, error growing polynomially with the condition number, or exponential time. Our near-optimal accuracy guarantee holds for any dataset with bounded statistical leverage and bounded residuals. Technically, we build on the approach of Brown et al. (2023) for private mean estimation, adding scaled noise to a carefully designed stable nonprivate estimator of the empirical regression vector.

Gavin Brown, Lydia Zakynthinou

Mean estimation is a fundamental task in statistics and a focus within differentially private statistical estimation. While univariate methods based on the Gaussian mechanism are widely used in practice, more advanced techniques such as the exponential mechanism over quantiles offer robustness and improved performance, especially for small sample sizes. Tukey depth mechanisms carry these advantages to multivariate data, providing similar strong theoretical guarantees. However, practical implementations fall behind these theoretical developments. In this work, we take the first step to bridge this gap by implementing the (Restricted) Tukey Depth Mechanism, a theoretically optimal mean estimator for multivariate Gaussian distributions, yielding improved practical methods for private mean estimation. Our implementations enable the use of these mechanisms for small sample sizes or low-dimensional data. Additionally, we implement variants of these mechanisms that use approximate versions of Tukey depth, trading off accuracy for faster computation. We demonstrate their efficiency in practice, showing that they are viable options for modest dimensions. Given their strong accuracy and robustness guarantees, we contend that they are competitive approaches for mean estimation in this regime. We explore future directions for improving the computational efficiency of these algorithms by leveraging fast polytope volume approximation techniques, paving the way for more accurate private mean estimation in higher dimensions.

Gavin Brown, Marco Gaboardi, Adam Smith et al.

We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/α^2$ samples from such a distribution with mean $μ$ and covariance $Σ$, our estimators output $\tildeμ$ such that $\| \tildeμ- μ\|_Σ \leq α$, where $\| \cdot \|_Σ$ is the Mahalanobis distance. All previous estimators with the same guarantee either require strong a priori bounds on the covariance matrix or require $Ω(d^{3/2})$ samples. Each of our estimators is based on a simple, general approach to designing differentially private mechanisms, but with novel technical steps to make the estimator private and sample-efficient. Our first estimator samples a point with approximately maximum Tukey depth using the exponential mechanism, but restricted to the set of points of large Tukey depth. Its accuracy guarantees hold even for data sets that have a small amount of adversarial corruption. Proving that this mechanism is private requires a novel analysis. Our second estimator perturbs the empirical mean of the data set with noise calibrated to the empirical covariance, without releasing the covariance itself. Its sample complexity guarantees hold more generally for subgaussian distributions, albeit with a slightly worse dependence on the privacy parameter. For both estimators, careful preprocessing of the data is required to satisfy differential privacy.

Gavin Brown, Mark Bun, Vitaly Feldman et al.

Modern machine learning models are complex and frequently encode surprising amounts of information about individual inputs. In extreme cases, complex models appear to memorize entire input examples, including seemingly irrelevant information (social security numbers from text, for example). In this paper, we aim to understand whether this sort of memorization is necessary for accurate learning. We describe natural prediction problems in which every sufficiently accurate training algorithm must encode, in the prediction model, essentially all the information about a large subset of its training examples. This remains true even when the examples are high-dimensional and have entropy much higher than the sample size, and even when most of that information is ultimately irrelevant to the task at hand. Further, our results do not depend on the training algorithm or the class of models used for learning. Our problems are simple and fairly natural variants of the next-symbol prediction and the cluster labeling tasks. These tasks can be seen as abstractions of text- and image-related prediction problems. To establish our results, we reduce from a family of one-way communication problems for which we prove new information complexity lower bounds. Additionally, we present synthetic-data experiments demonstrating successful attacks on logistic regression and neural network classifiers.

Gavin Brown, Shlomi Hod, Iden Kalemaj

Deployed supervised machine learning models make predictions that interact with and influence the world. This phenomenon is called performative prediction by Perdomo et al. (ICML 2020). It is an ongoing challenge to understand the influence of such predictions as well as design tools so as to control that influence. We propose a theoretical framework where the response of a target population to the deployed classifier is modeled as a function of the classifier and the current state (distribution) of the population. We show necessary and sufficient conditions for convergence to an equilibrium of two retraining algorithms, repeated risk minimization and a lazier variant. Furthermore, convergence is near an optimal classifier. We thus generalize results of Perdomo et al., whose performativity framework does not assume any dependence on the state of the target population. A particular phenomenon captured by our model is that of distinct groups that acquire information and resources at different rates to be able to respond to the latest deployed classifier. We study this phenomenon theoretically and empirically.

Georgiana Neculae, Oliver Rhodes, Gavin Brown

This paper demonstrates how to construct ensembles of spiking neural networks producing state-of-the-art results, achieving classification accuracies of 98.71%, 100.0%, and 99.09%, on the MNIST, NMNIST and DVS Gesture datasets respectively. Furthermore, this performance is achieved using simplified individual models, with ensembles containing less than 50% of the parameters of published reference models. We provide comprehensive exploration on the effect of spike train interpretation methods, and derive the theoretical methodology for combining model predictions such that performance improvements are guaranteed for spiking ensembles. For this, we formalize spiking neural networks as GLM predictors, identifying a suitable representation for their target domain. Further, we show how the diversity of our spiking ensembles can be measured using the Ambiguity Decomposition. The work demonstrates how ensembling can overcome the challenges of producing individual SNN models which can compete with traditional deep neural networks, and creates systems with fewer trainable parameters and smaller memory footprints, opening the door to low-power edge applications, e.g. implemented on neuromorphic hardware.

Nikolaos Nikolaou, Henry Reeve, Gavin Brown

The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training examples as possible with maximal confidence --has been known to construct models with good generalization guarantees. This work gives an information-theoretic interpretation of a margin maximizing model on a noiseless training dataset as one that achieves lossless maximal compression of said dataset -- i.e. extracts from the features all the useful information for predicting the label and no more. The connection offers new insights on generalization in supervised machine learning, showing margin maximization as a special case (that of classification) of a more general principle and explains the success and potential limitations of popular learning algorithms like gradient boosting. We support our observations with theoretical arguments and empirical evidence and identify interesting directions for future work.

Nikolaos Nikolaou, Joseph Mellor, Nikunj C. Oza et al.

Probability estimates generated by boosting ensembles are poorly calibrated because of the margin maximization nature of the algorithm. The outputs of the ensemble need to be properly calibrated before they can be used as probability estimates. In this work, we demonstrate that online boosting is also prone to producing distorted probability estimates. In batch learning, calibration is achieved by reserving part of the training data for training the calibrator function. In the online setting, a decision needs to be made on each round: shall the new example(s) be used to update the parameters of the ensemble or those of the calibrator. We proceed to resolve this decision with the aid of bandit optimization algorithms. We demonstrate superior performance to uncalibrated and naively-calibrated on-line boosting ensembles in terms of probability estimation. Our proposed mechanism can be easily adapted to other tasks(e.g. cost-sensitive classification) and is robust to the choice of hyperparameters of both the calibrator and the ensemble.

Andrew M. Webb, Charles Reynolds, Wenlin Chen et al.

End-to-End training (E2E) is becoming more and more popular to train complex Deep Network architectures. An interesting question is whether this trend will continue-are there any clear failure cases for E2E training? We study this question in depth, for the specific case of E2E training an ensemble of networks. Our strategy is to blend the gradient smoothly in between two extremes: from independent training of the networks, up to to full E2E training. We find clear failure cases, where over-parameterized models cannot be trained E2E. A surprising result is that the optimum can sometimes lie in between the two, neither an ensemble or an E2E system. The work also uncovers links to Dropout, and raises questions around the nature of ensemble diversity and multi-branch networks.

Huang Xiao, Battista Biggio, Gavin Brown et al.

Learning in adversarial settings is becoming an important task for application domains where attackers may inject malicious data into the training set to subvert normal operation of data-driven technologies. Feature selection has been widely used in machine learning for security applications to improve generalization and computational efficiency, although it is not clear whether its use may be beneficial or even counterproductive when training data are poisoned by intelligent attackers. In this work, we shed light on this issue by providing a framework to investigate the robustness of popular feature selection methods, including LASSO, ridge regression and the elastic net. Our results on malware detection show that feature selection methods can be significantly compromised under attack (we can reduce LASSO to almost random choices of feature sets by careful insertion of less than 5% poisoned training samples), highlighting the need for specific countermeasures.

Henry WJ Reeve, Joe Mellor, Gavin Brown

In this paper we propose and explore the k-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates. We focus on a setting where the covariates are supported on a metric space of low intrinsic dimension, such as a manifold embedded within a high dimensional ambient feature space. The algorithm is conceptually simple and straightforward to implement. The k-Nearest Neighbour UCB algorithm does not require prior knowledge of the either the intrinsic dimension of the marginal distribution or the time horizon. We prove a regret bound for the k-Nearest Neighbour UCB algorithm which is minimax optimal up to logarithmic factors. In particular, the algorithm automatically takes advantage of both low intrinsic dimensionality of the marginal distribution over the covariates and low noise in the data, expressed as a margin condition. In addition, focusing on the case of bounded rewards, we give corresponding regret bounds for the k-Nearest Neighbour KL-UCB algorithm, which is an analogue of the KL-UCB algorithm adapted to the setting of multi-armed bandits with covariates. Finally, we present empirical results which demonstrate the ability of both the k-Nearest Neighbour UCB and k-Nearest Neighbour KL-UCB to take advantage of situations where the data is supported on an unknown sub-manifold of a high-dimensional feature space.

Henry WJ Reeve, Gavin Brown

Ensemble methods are a cornerstone of modern machine learning. The performance of an ensemble depends crucially upon the level of diversity between its constituent learners. This paper establishes a connection between diversity and degrees of freedom (i.e. the capacity of the model), showing that diversity may be viewed as a form of inverse regularisation. This is achieved by focusing on a previously published algorithm Negative Correlation Learning (NCL), in which model diversity is explicitly encouraged through a diversity penalty term in the loss function. We provide an exact formula for the effective degrees of freedom in an NCL ensemble with fixed basis functions, showing that it is a continuous, convex and monotonically increasing function of the diversity parameter. We demonstrate a connection to Tikhonov regularisation and show that, with an appropriately chosen diversity parameter, an NCL ensemble can always outperform the unregularised ensemble in the presence of noise. We demonstrate the practical utility of our approach by deriving a method to efficiently tune the diversity parameter. Finally, we use a Monte-Carlo estimator to extend the connection between diversity and degrees of freedom to ensembles of deep neural networks.

Henry WJ Reeve, Gavin Brown

We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth manifold, in a cost-sensitive setting. This generalises a classic result of Audibert and Tsybakov. Building upon recent work of Chaudhuri and Dasgupta we prove that these minimax rates are attained by the approximate nearest neighbour algorithm, where neighbours are computed in a randomly projected low-dimensional space. In addition, we give a bound on the number of dimensions required for the projection which depends solely upon the reach and dimension of the manifold, combined with the regularity of the marginal.

Marco Melis, Ambra Demontis, Battista Biggio et al.

Deep neural networks have been widely adopted in recent years, exhibiting impressive performances in several application domains. It has however been shown that they can be fooled by adversarial examples, i.e., images altered by a barely-perceivable adversarial noise, carefully crafted to mislead classification. In this work, we aim to evaluate the extent to which robot-vision systems embodying deep-learning algorithms are vulnerable to adversarial examples, and propose a computationally efficient countermeasure to mitigate this threat, based on rejecting classification of anomalous inputs. We then provide a clearer understanding of the safety properties of deep networks through an intuitive empirical analysis, showing that the mapping learned by such networks essentially violates the smoothness assumption of learning algorithms. We finally discuss the main limitations of this work, including the creation of real-world adversarial examples, and sketch promising research directions.

Konstantinos Sechidis, Emily Turner, Paul D. Metcalfe et al.

We study information theoretic methods for ranking biomarkers. In clinical trials there are two, closely related, types of biomarkers: predictive and prognostic, and disentangling them is a key challenge. Our first step is to phrase biomarker ranking in terms of optimizing an information theoretic quantity. This formalization of the problem will enable us to derive rankings of predictive/prognostic biomarkers, by estimating different, high dimensional, conditional mutual information terms. To estimate these terms, we suggest efficient low dimensional approximations, and we derive an empirical Bayes estimator, which is suitable for small or sparse datasets. Finally, we introduce a new visualisation tool that captures the prognostic and the predictive strength of a set of biomarkers. We believe this representation will prove to be a powerful tool in biomarker discovery.

Henry W J Reeve, Gavin Brown

We introduce the concept of a Modular Autoencoder (MAE), capable of learning a set of diverse but complementary representations from unlabelled data, that can later be used for supervised tasks. The learning of the representations is controlled by a trade off parameter, and we show on six benchmark datasets the optimum lies between two extremes: a set of smaller, independent autoencoders each with low capacity, versus a single monolithic encoding, outperforming an appropriate baseline. In the present paper we explore the special case of linear MAE, and derive an SVD-based algorithm which converges several orders of magnitude faster than gradient descent.