Matthew Blaschko

CV
h-index76
26papers
4,764citations
Novelty44%
AI Score35

26 Papers

CVJun 3, 2022
Metrics reloaded: Recommendations for image analysis validation

Lena Maier-Hein, Annika Reinke, Patrick Godau et al. · utoronto

Increasing evidence shows that flaws in machine learning (ML) algorithm validation are an underestimated global problem. Particularly in automatic biomedical image analysis, chosen performance metrics often do not reflect the domain interest, thus failing to adequately measure scientific progress and hindering translation of ML techniques into practice. To overcome this, our large international expert consortium created Metrics Reloaded, a comprehensive framework guiding researchers in the problem-aware selection of metrics. Following the convergence of ML methodology across application domains, Metrics Reloaded fosters the convergence of validation methodology. The framework was developed in a multi-stage Delphi process and is based on the novel concept of a problem fingerprint - a structured representation of the given problem that captures all aspects that are relevant for metric selection, from the domain interest to the properties of the target structure(s), data set and algorithm output. Based on the problem fingerprint, users are guided through the process of choosing and applying appropriate validation metrics while being made aware of potential pitfalls. Metrics Reloaded targets image analysis problems that can be interpreted as a classification task at image, object or pixel level, namely image-level classification, object detection, semantic segmentation, and instance segmentation tasks. To improve the user experience, we implemented the framework in the Metrics Reloaded online tool, which also provides a point of access to explore weaknesses, strengths and specific recommendations for the most common validation metrics. The broad applicability of our framework across domains is demonstrated by an instantiation for various biological and medical image analysis use cases.

CVJul 14, 2023Code
Multimodal Distillation for Egocentric Action Recognition

Gorjan Radevski, Dusan Grujicic, Marie-Francine Moens et al.

The focal point of egocentric video understanding is modelling hand-object interactions. Standard models, e.g. CNNs or Vision Transformers, which receive RGB frames as input perform well. However, their performance improves further by employing additional input modalities that provide complementary cues, such as object detections, optical flow, audio, etc. The added complexity of the modality-specific modules, on the other hand, makes these models impractical for deployment. The goal of this work is to retain the performance of such a multimodal approach, while using only the RGB frames as input at inference time. We demonstrate that for egocentric action recognition on the Epic-Kitchens and the Something-Something datasets, students which are taught by multimodal teachers tend to be more accurate and better calibrated than architecturally equivalent models trained on ground truth labels in a unimodal or multimodal fashion. We further adopt a principled multimodal knowledge distillation framework, allowing us to deal with issues which occur when applying multimodal knowledge distillation in a naive manner. Lastly, we demonstrate the achieved reduction in computational complexity, and show that our approach maintains higher performance with the reduction of the number of input views. We release our code at https://github.com/gorjanradevski/multimodal-distillation.

CVFeb 3, 2023
Understanding metric-related pitfalls in image analysis validation

Annika Reinke, Minu D. Tizabi, Michael Baumgartner et al.

Validation metrics are key for the reliable tracking of scientific progress and for bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that particularly in image analysis, metrics are often chosen inadequately in relation to the underlying research problem. This could be attributed to a lack of accessibility of metric-related knowledge: While taking into account the individual strengths, weaknesses, and limitations of validation metrics is a critical prerequisite to making educated choices, the relevant knowledge is currently scattered and poorly accessible to individual researchers. Based on a multi-stage Delphi process conducted by a multidisciplinary expert consortium as well as extensive community feedback, the present work provides the first reliable and comprehensive common point of access to information on pitfalls related to validation metrics in image analysis. Focusing on biomedical image analysis but with the potential of transfer to other fields, the addressed pitfalls generalize across application domains and are categorized according to a newly created, domain-agnostic taxonomy. To facilitate comprehension, illustrations and specific examples accompany each pitfall. As a structured body of information accessible to researchers of all levels of expertise, this work enhances global comprehension of a key topic in image analysis validation.

CVOct 9, 2022
Students taught by multimodal teachers are superior action recognizers

Gorjan Radevski, Dusan Grujicic, Matthew Blaschko et al.

The focal point of egocentric video understanding is modelling hand-object interactions. Standard models -- CNNs, Vision Transformers, etc. -- which receive RGB frames as input perform well, however, their performance improves further by employing additional modalities such as object detections, optical flow, audio, etc. as input. The added complexity of the required modality-specific modules, on the other hand, makes these models impractical for deployment. The goal of this work is to retain the performance of such multimodal approaches, while using only the RGB images as input at inference time. Our approach is based on multimodal knowledge distillation, featuring a multimodal teacher (in the current experiments trained only using object detections, optical flow and RGB frames) and a unimodal student (using only RGB frames as input). We present preliminary results which demonstrate that the resulting model -- distilled from a multimodal teacher -- significantly outperforms the baseline RGB model (trained without knowledge distillation), as well as an omnivorous version of itself (trained on all modalities jointly), in both standard and compositional action recognition.

LGNov 11, 2024Code
Balancing Multimodal Training Through Game-Theoretic Regularization

Konstantinos Kontras, Thomas Strypsteen, Christos Chatzichristos et al.

Multimodal learning holds promise for richer information extraction by capturing dependencies across data sources. Yet, current training methods often underperform due to modality competition, a phenomenon where modalities contend for training resources leaving some underoptimized. This raises a pivotal question: how can we address training imbalances, ensure adequate optimization across all modalities, and achieve consistent performance improvements as we transition from unimodal to multimodal data? This paper proposes the Multimodal Competition Regularizer (MCR), inspired by a mutual information (MI) decomposition designed to prevent the adverse effects of competition in multimodal training. Our key contributions are: 1) A game-theoretic framework that adaptively balances modality contributions by encouraging each to maximize its informative role in the final prediction 2) Refining lower and upper bounds for each MI term to enhance the extraction of both task-relevant unique and shared information across modalities. 3) Proposing latent space permutations for conditional MI estimation, significantly improving computational efficiency. MCR outperforms all previously suggested training strategies and simple baseline, clearly demonstrating that training modalities jointly leads to important performance gains on both synthetic and large real-world datasets. We release our code and models at https://github.com/kkontras/MCR.

LGOct 15, 2020Code
R-GAP: Recursive Gradient Attack on Privacy

Junyi Zhu, Matthew Blaschko

Federated learning frameworks have been regarded as a promising approach to break the dilemma between demands on privacy and the promise of learning from large collections of distributed data. Many such frameworks only ask collaborators to share their local update of a common model, i.e. gradients with respect to locally stored data, instead of exposing their raw data to other collaborators. However, recent optimization-based gradient attacks show that raw data can often be accurately recovered from gradients. It has been shown that minimizing the Euclidean distance between true gradients and those calculated from estimated data is often effective in fully recovering private data. However, there is a fundamental lack of theoretical understanding of how and when gradients can lead to unique recovery of original data. Our research fills this gap by providing a closed-form recursive procedure to recover data from gradients in deep neural networks. We name it Recursive Gradient Attack on Privacy (R-GAP). Experimental results demonstrate that R-GAP works as well as or even better than optimization-based approaches at a fraction of the computation under certain conditions. Additionally, we propose a Rank Analysis method, which can be used to estimate the risk of gradient attacks inherent in certain network architectures, regardless of whether an optimization-based or closed-form-recursive attack is used. Experimental results demonstrate the utility of the rank analysis towards improving the network's security. Source code is available for download from https://github.com/JunyiZhu-AI/R-GAP.

MLJun 15, 2014Code
A low variance consistent test of relative dependency

Wacha Bounliphone, Arthur Gretton, Arthur Tenenhaus et al.

We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more dependent on a first target variable or a second. Dependence is measured via the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of empirical dependence measures (source-target 1, source-target 2). We test whether the first dependence measure is significantly larger than the second. Modeling the covariance between these HSIC statistics leads to a provably more powerful test than the construction of independent HSIC statistics by sub-sampling. The resulting test is consistent and unbiased, and (being based on U-statistics) has favorable convergence properties. The test can be computed in quadratic time, matching the computational complexity of standard empirical HSIC estimators. The effectiveness of the test is demonstrated on several real-world problems: we identify language groups from a multilingual corpus, and we prove that tumor location is more dependent on gene expression than chromosomal imbalances. Source code is available for download at https://github.com/wbounliphone/reldep.

MMMay 13, 2024
Improving Multimodal Learning with Multi-Loss Gradient Modulation

Konstantinos Kontras, Christos Chatzichristos, Matthew Blaschko et al.

Learning from multiple modalities, such as audio and video, offers opportunities for leveraging complementary information, enhancing robustness, and improving contextual understanding and performance. However, combining such modalities presents challenges, especially when modalities differ in data structure, predictive contribution, and the complexity of their learning processes. It has been observed that one modality can potentially dominate the learning process, hindering the effective utilization of information from other modalities and leading to sub-optimal model performance. To address this issue the vast majority of previous works suggest to assess the unimodal contributions and dynamically adjust the training to equalize them. We improve upon previous work by introducing a multi-loss objective and further refining the balancing process, allowing it to dynamically adjust the learning pace of each modality in both directions, acceleration and deceleration, with the ability to phase out balancing effects upon convergence. We achieve superior results across three audio-video datasets: on CREMA-D, models with ResNet backbone encoders surpass the previous best by 1.9% to 12.4%, and Conformer backbone models deliver improvements ranging from 2.8% to 14.1% across different fusion methods. On AVE, improvements range from 2.7% to 7.7%, while on UCF101, gains reach up to 6.1%.

CVMay 21, 2024
Multimodal Adaptive Inference for Document Image Classification with Anytime Early Exiting

Omar Hamed, Souhail Bakkali, Marie-Francine Moens et al.

This work addresses the need for a balanced approach between performance and efficiency in scalable production environments for visually-rich document understanding (VDU) tasks. Currently, there is a reliance on large document foundation models that offer advanced capabilities but come with a heavy computational burden. In this paper, we propose a multimodal early exit (EE) model design that incorporates various training strategies, exit layer types and placements. Our goal is to achieve a Pareto-optimal balance between predictive performance and efficiency for multimodal document image classification. Through a comprehensive set of experiments, we compare our approach with traditional exit policies and showcase an improved performance-efficiency trade-off. Our multimodal EE design preserves the model's predictive capabilities, enhancing both speed and latency. This is achieved through a reduction of over 20% in latency, while fully retaining the baseline accuracy. This research represents the first exploration of multimodal EE design within the VDU community, highlighting as well the effectiveness of calibration in improving confidence scores for exiting at different layers. Overall, our findings contribute to practical VDU applications by enhancing both performance and efficiency.

IVApr 26, 2025
Surgeons vs. Computer Vision: A comparative analysis on surgical phase recognition capabilities

Marco Mezzina, Pieter De Backer, Tom Vercauteren et al.

Purpose: Automated Surgical Phase Recognition (SPR) uses Artificial Intelligence (AI) to segment the surgical workflow into its key events, functioning as a building block for efficient video review, surgical education as well as skill assessment. Previous research has focused on short and linear surgical procedures and has not explored if temporal context influences experts' ability to better classify surgical phases. This research addresses these gaps, focusing on Robot-Assisted Partial Nephrectomy (RAPN) as a highly non-linear procedure. Methods: Urologists of varying expertise were grouped and tasked to indicate the surgical phase for RAPN on both single frames and video snippets using a custom-made web platform. Participants reported their confidence levels and the visual landmarks used in their decision-making. AI architectures without and with temporal context as trained and benchmarked on the Cholec80 dataset were subsequently trained on this RAPN dataset. Results: Video snippets and presence of specific visual landmarks improved phase classification accuracy across all groups. Surgeons displayed high confidence in their classifications and outperformed novices, who struggled discriminating phases. The performance of the AI models is comparable to the surgeons in the survey, with improvements when temporal context was incorporated in both cases. Conclusion: SPR is an inherently complex task for expert surgeons and computer vision, where both perform equally well when given the same context. Performance increases when temporal information is provided. Surgical tools and organs form the key landmarks for human interpretation and are expected to shape the future of automated SPR.

CVJun 12, 2024
DistilDoc: Knowledge Distillation for Visually-Rich Document Applications

Jordy Van Landeghem, Subhajit Maity, Ayan Banerjee et al.

This work explores knowledge distillation (KD) for visually-rich document (VRD) applications such as document layout analysis (DLA) and document image classification (DIC). While VRD research is dependent on increasingly sophisticated and cumbersome models, the field has neglected to study efficiency via model compression. Here, we design a KD experimentation methodology for more lean, performant models on document understanding (DU) tasks that are integral within larger task pipelines. We carefully selected KD strategies (response-based, feature-based) for distilling knowledge to and from backbones with different architectures (ResNet, ViT, DiT) and capacities (base, small, tiny). We study what affects the teacher-student knowledge gap and find that some methods (tuned vanilla KD, MSE, SimKD with an apt projector) can consistently outperform supervised student training. Furthermore, we design downstream task setups to evaluate covariate shift and the robustness of distilled DLA models on zero-shot layout-aware document visual question answering (DocVQA). DLA-KD experiments result in a large mAP knowledge gap, which unpredictably translates to downstream robustness, accentuating the need to further explore how to efficiently obtain more semantic document layout awareness.

CVMay 15, 2023
Document Understanding Dataset and Evaluation (DUDE)

Jordy Van Landeghem, Rubén Tito, Łukasz Borchmann et al.

We call on the Document AI (DocAI) community to reevaluate current methodologies and embrace the challenge of creating more practically-oriented benchmarks. Document Understanding Dataset and Evaluation (DUDE) seeks to remediate the halted research progress in understanding visually-rich documents (VRDs). We present a new dataset with novelties related to types of questions, answers, and document layouts based on multi-industry, multi-domain, and multi-page VRDs of various origins, and dates. Moreover, we are pushing the boundaries of current methods by creating multi-task and multi-domain evaluation setups that more accurately simulate real-world situations where powerful generalization and adaptation under low-resource settings are desired. DUDE aims to set a new standard as a more practical, long-standing benchmark for the community, and we hope that it will lead to future extensions and contributions that address real-world challenges. Finally, our work illustrates the importance of finding more efficient ways to model language, images, and layout in DocAI.

AIDec 10, 2021
Predicting Physical World Destinations for Commands Given to Self-Driving Cars

Dusan Grujicic, Thierry Deruyttere, Marie-Francine Moens et al.

In recent years, we have seen significant steps taken in the development of self-driving cars. Multiple companies are starting to roll out impressive systems that work in a variety of settings. These systems can sometimes give the impression that full self-driving is just around the corner and that we would soon build cars without even a steering wheel. The increase in the level of autonomy and control given to an AI provides an opportunity for new modes of human-vehicle interaction. However, surveys have shown that giving more control to an AI in self-driving cars is accompanied by a degree of uneasiness by passengers. In an attempt to alleviate this issue, recent works have taken a natural language-oriented approach by allowing the passenger to give commands that refer to specific objects in the visual scene. Nevertheless, this is only half the task as the car should also understand the physical destination of the command, which is what we focus on in this paper. We propose an extension in which we annotate the 3D destination that the car needs to reach after executing the given command and evaluate multiple different baselines on predicting this destination location. Additionally, we introduce a model that outperforms the prior works adapted for this particular setting.

IVApr 12, 2021
Common Limitations of Image Processing Metrics: A Picture Story

Annika Reinke, Minu D. Tizabi, Carole H. Sudre et al.

While the importance of automatic image analysis is continuously increasing, recent meta-research revealed major flaws with respect to algorithm validation. Performance metrics are particularly key for meaningful, objective, and transparent performance assessment and validation of the used automatic algorithms, but relatively little attention has been given to the practical pitfalls when using specific metrics for a given image analysis task. These are typically related to (1) the disregard of inherent metric properties, such as the behaviour in the presence of class imbalance or small target structures, (2) the disregard of inherent data set properties, such as the non-independence of the test cases, and (3) the disregard of the actual biomedical domain interest that the metrics should reflect. This living dynamically document has the purpose to illustrate important limitations of performance metrics commonly applied in the field of image analysis. In this context, it focuses on biomedical image analysis problems that can be phrased as image-level classification, semantic segmentation, instance segmentation, or object detection task. The current version is based on a Delphi process on metrics conducted by an international consortium of image analysis experts from more than 60 institutions worldwide.

CVSep 18, 2020
Commands 4 Autonomous Vehicles (C4AV) Workshop Summary

Thierry Deruyttere, Simon Vandenhende, Dusan Grujicic et al.

The task of visual grounding requires locating the most relevant region or object in an image, given a natural language query. So far, progress on this task was mostly measured on curated datasets, which are not always representative of human spoken language. In this work, we deviate from recent, popular task settings and consider the problem under an autonomous vehicle scenario. In particular, we consider a situation where passengers can give free-form natural language commands to a vehicle which can be associated with an object in the street scene. To stimulate research on this topic, we have organized the \emph{Commands for Autonomous Vehicles} (C4AV) challenge based on the recent \emph{Talk2Car} dataset (URL: https://www.aicrowd.com/challenges/eccv-2020-commands-4-autonomous-vehicles). This paper presents the results of the challenge. First, we compare the used benchmark against existing datasets for visual grounding. Second, we identify the aspects that render top-performing models successful, and relate them to existing state-of-the-art models for visual grounding, in addition to detecting potential failure cases by evaluating on carefully selected subsets. Finally, we discuss several possibilities for future work.

IVMar 4, 2020
Semixup: In- and Out-of-Manifold Regularization for Deep Semi-Supervised Knee Osteoarthritis Severity Grading from Plain Radiographs

Huy Hoang Nguyen, Simo Saarakkala, Matthew Blaschko et al.

Knee osteoarthritis (OA) is one of the highest disability factors in the world. This musculoskeletal disorder is assessed from clinical symptoms, and typically confirmed via radiographic assessment. This visual assessment done by a radiologist requires experience, and suffers from moderate to high inter-observer variability. The recent literature has shown that deep learning methods can reliably perform the OA severity assessment according to the gold standard Kellgren-Lawrence (KL) grading system. However, these methods require large amounts of labeled data, which are costly to obtain. In this study, we propose the Semixup algorithm, a semi-supervised learning (SSL) approach to leverage unlabeled data. Semixup relies on consistency regularization using in- and out-of-manifold samples, together with interpolated consistency. On an independent test set, our method significantly outperformed other state-of-the-art SSL methods in most cases. Finally, when compared to a well-tuned fully supervised baseline that yielded a balanced accuracy (BA) of $70.9\pm0.8%$ on the test set, Semixup had comparable performance -- BA of $71\pm0.8%$ $(p=0.368)$ while requiring $6$ times less labeled data. These results show that our proposed SSL method allows building fully automatic OA severity assessment tools with datasets that are available outside research settings.

CVNov 5, 2019
Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice

Jeroen Bertels, Tom Eelbode, Maxim Berman et al.

The Dice score and Jaccard index are commonly used metrics for the evaluation of segmentation tasks in medical imaging. Convolutional neural networks trained for image segmentation tasks are usually optimized for (weighted) cross-entropy. This introduces an adverse discrepancy between the learning optimization objective (the loss) and the end target metric. Recent works in computer vision have proposed soft surrogates to alleviate this discrepancy and directly optimize the desired metric, either through relaxations (soft-Dice, soft-Jaccard) or submodular optimization (Lovász-softmax). The aim of this study is two-fold. First, we investigate the theoretical differences in a risk minimization framework and question the existence of a weighted cross-entropy loss with weights theoretically optimized to surrogate Dice or Jaccard. Second, we empirically investigate the behavior of the aforementioned loss functions w.r.t. evaluation with Dice score and Jaccard index on five medical segmentation tasks. Through the application of relative approximation bounds, we show that all surrogates are equivalent up to a multiplicative factor, and that no optimal weighting of cross-entropy exists to approximate Dice or Jaccard measures. We validate these findings empirically and show that, while it is important to opt for one of the target metric surrogates rather than a cross-entropy-based loss, the choice of the surrogate does not make a statistical difference on a wide range of medical segmentation tasks.

CVMar 11, 2019
Generating superpixels using deep image representations

Thomas Verelst, Matthew Blaschko, Maxim Berman

Superpixel algorithms are a common pre-processing step for computer vision algorithms such as segmentation, object tracking and localization. Many superpixel methods only rely on colors features for segmentation, limiting performance in low-contrast regions and applicability to infrared or medical images where object boundaries have wide appearance variability. We study the inclusion of deep image features in the SLIC superpixel algorithm to exploit higher-level image representations. In addition, we devise a trainable superpixel algorithm, yielding an intermediate domain-specific image representation that can be applied to different tasks. A clustering-based superpixel algorithm is transformed into a pixel-wise classification task and superpixel training data is derived from semantic segmentation datasets. Our results demonstrate that this approach is able to improve superpixel quality consistently.

LGSep 17, 2018
Scattering Networks for Hybrid Representation Learning

Edouard Oyallon, Sergey Zagoruyko, Gabriel Huang et al.

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making progress towards constructing more interpretable CNNs. For supervised learning, we demonstrate that the early layers of CNNs do not necessarily need to be learned, and can be replaced with a scattering network instead. Indeed, using hybrid architectures, we achieve the best results with predefined representations to-date, while being competitive with end-to-end learned CNNs. Specifically, even applying a shallow cascade of small-windowed scattering coefficients followed by 1$\times$1-convolutions results in AlexNet accuracy on the ILSVRC2012 classification task. Moreover, by combining scattering networks with deep residual networks, we achieve a single-crop top-5 error of 11.4% on ILSVRC2012. Also, we show they can yield excellent performance in the small sample regime on CIFAR-10 and STL-10 datasets, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. For unsupervised learning, scattering coefficients can be a competitive representation that permits image recovery. We use this fact to train hybrid GANs to generate images. Finally, we empirically analyze several properties related to stability and reconstruction of images from scattering coefficients.

MLMay 20, 2016
Learning to Discover Sparse Graphical Models

Eugene Belilovsky, Kyle Kastner, Gaël Varoquaux et al.

We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures. Popular methods rely on estimating a penalized maximum likelihood of the precision matrix. However, in these approaches structure recovery is an indirect consequence of the data-fit term, the penalty can be difficult to adapt for domain-specific knowledge, and the inference is computationally demanding. By contrast, it may be easier to generate training samples of data that arise from graphs with the desired structure properties. We propose here to leverage this latter source of information as training data to learn a function, parametrized by a neural network that maps empirical covariance matrices to estimated graph structures. Learning this function brings two benefits: it implicitly models the desired structure or sparsity properties to form suitable priors, and it can be tailored to the specific problem of edge structure discovery, rather than maximizing data likelihood. Applying this framework, we find our learnable graph-discovery method trained on synthetic data generalizes well: identifying relevant edges in both synthetic and real data, completely unknown at training time. We find that on genetics, brain imaging, and simulation data we obtain performance generally superior to analytical methods.

MLApr 12, 2016
A Convex Surrogate Operator for General Non-Modular Loss Functions

Jiaqian Yu, Matthew Blaschko

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex surrogate for general non-modular loss functions is introduced, which provides for the first time a tractable solution for loss functions that are neither super-modular nor submodular. This convex surro-gate is based on a submodular-supermodular decomposition for which the existence and uniqueness is proven in this paper. It takes the sum of two convex surrogates that separately bound the supermodular component and the submodular component using slack-rescaling and the Lov{á}sz hinge, respectively. It is further proven that this surrogate is convex , piecewise linear, an extension of the loss function, and for which subgradient computation is polynomial time. Empirical results are reported on a non-submodular loss based on the S{ø}rensen-Dice difference function, and a real-world face track dataset with tens of thousands of frames, demonstrating the improved performance, efficiency, and scalabil-ity of the novel convex surrogate.

MLApr 6, 2016
A U-statistic Approach to Hypothesis Testing for Structure Discovery in Undirected Graphical Models

Wacha Bounliphone, Matthew Blaschko

Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions, an edge between two variables is present if and only if the corresponding entry in the precision matrix is non-zero. For a finite sample estimate of the precision matrix, entries close to zero may be due to low sample effects, or due to an actual association between variables; these two cases are not readily distinguishable. %Fisher provided a hypothesis test based on a parametric approximation to the distribution of an entry in the precision matrix of a Gaussian distribution, but this may not provide valid upper bounds on $p$-values for non-Gaussian distributions. Many related works on this topic consider potentially restrictive distributional or sparsity assumptions that may not apply to a data sample of interest, and direct estimation of the uncertainty of an estimate of the precision matrix for general distributions remains challenging. Consequently, we make use of results for $U$-statistics and apply them to the covariance matrix. By probabilistically bounding the distortion of the covariance matrix, we can apply Weyl's theorem to bound the distortion of the precision matrix, yielding a conservative, but sound test threshold for a much wider class of distributions than considered in previous works. The resulting test enables one to answer with statistical significance whether an edge is present in the graph, and convergence results are known for a wide range of distributions. The computational complexities is linear in the sample size enabling the application of the test to large data samples for which computation time becomes a limiting factor. We experimentally validate the correctness and scalability of the test on multivariate distributions for which the distributional assumptions of competing tests result in underestimates of the false positive ratio. By contrast, the proposed test remains sound, promising to be a useful tool for hypothesis testing for diverse real-world problems.

MLDec 24, 2015
The Lovász Hinge: A Novel Convex Surrogate for Submodular Losses

Jiaqian Yu, Matthew Blaschko

Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for non-supermodular loss functions. We propose instead a novel surrogate loss function for submodular losses, the Lovász hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. We prove that the Lovász hinge is convex and yields an extension. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through several set prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets.

LGJul 8, 2013
B-tests: Low Variance Kernel Two-Sample Tests

Wojciech Zaremba, Arthur Gretton, Matthew Blaschko

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computation time. In this respect, the $B$-test family combines favorable properties of previously proposed MMD two-sample tests: B-tests are more powerful than a linear time test where blocks are just pairs of samples, yet they are more computationally efficient than a quadratic time test where a single large block incorporating all the samples is used to compute a U-statistic. A further important advantage of the B-tests is their asymptotically Normal null distribution: this is by contrast with the U-statistic, which is degenerate under the null hypothesis, and for which estimates of the null distribution are computationally demanding. Recent results on kernel selection for hypothesis testing transfer seamlessly to the B-tests, yielding a means to optimize test power via kernel choice.

CVJun 21, 2013
Fine-Grained Visual Classification of Aircraft

Subhransu Maji, Esa Rahtu, Juho Kannala et al.

This paper introduces FGVC-Aircraft, a new dataset containing 10,000 images of aircraft spanning 100 aircraft models, organised in a three-level hierarchy. At the finer level, differences between models are often subtle but always visually measurable, making visual recognition challenging but possible. A benchmark is obtained by defining corresponding classification tasks and evaluation protocols, and baseline results are presented. The construction of this dataset was made possible by the work of aircraft enthusiasts, a strategy that can extend to the study of number of other object classes. Compared to the domains usually considered in fine-grained visual classification (FGVC), for example animals, aircraft are rigid and hence less deformable. They, however, present other interesting modes of variation, including purpose, size, designation, structure, historical style, and branding.

LGMar 26, 2013
A Note on k-support Norm Regularized Risk Minimization

Matthew Blaschko

The k-support norm has been recently introduced to perform correlated sparsity regularization. Although Argyriou et al. only reported experiments using squared loss, here we apply it to several other commonly used settings resulting in novel machine learning algorithms with interesting and familiar limit cases. Source code for the algorithms described here is available.