Tomáš Pevný

Rony Abecidan, Vincent Itier, Jérémie Boulanger et al.

Within an operational framework, covers used by a steganographer are likely to come from different sensors and different processing pipelines than the ones used by researchers for training their steganalysis models. Thus, a performance gap is unavoidable when it comes to out-of-distributions covers, an extremely frequent scenario called Cover Source Mismatch (CSM). Here, we explore a grid of processing pipelines to study the origins of CSM, to better understand it, and to better tackle it. A set-covering greedy algorithm is used to select representative pipelines minimizing the maximum regret between the representative and the pipelines within the set. Our main contribution is a methodology for generating relevant bases able to tackle operational CSM. Experimental validation highlights that, for a given number of training samples, our set covering selection is a better strategy than selecting random pipelines or using all the available pipelines. Our analysis also shows that parameters as denoising, sharpening, and downsampling are very important to foster diversity. Finally, different benchmarks for classical and wild databases show the good generalization property of the extracted databases. Additional resources are available at github.com/RonyAbecidan/HolisticSteganalysisWithSetCovering.

Rony Abecidan, Vincent Itier, Jérémie Boulanger et al.

In operational scenarios, steganographers use sets of covers from various sensors and processing pipelines that differ significantly from those used by researchers to train steganalysis models. This leads to an inevitable performance gap when dealing with out-of-distribution covers, commonly referred to as Cover Source Mismatch (CSM). In this study, we consider the scenario where test images are processed using the same pipeline. However, knowledge regarding both the labels and the balance between cover and stego is missing. Our objective is to identify a training dataset that allows for maximum generalization to our target. By exploring a grid of processing pipelines fostering CSM, we discovered a geometrical metric based on the chordal distance between subspaces spanned by DCTr features, that exhibits high correlation with operational regret while being not affected by the cover-stego balance. Our contribution lies in the development of a strategy that enables the selection or derivation of customized training datasets, enhancing the overall generalization performance for a given target. Experimental validation highlights that our geometry-based optimization strategy outperforms traditional atomistic methods given reasonable assumptions. Additional resources are available at github.com/RonyAbecidan/LeveragingGeometrytoMitigateCSM.

Rony Abecidan, Vincent Itier, Jérémie Boulanger et al.

Steganalysis models excel on benchmark datasets but struggle in the wild when analyzed images are produced by a processing pipeline unseen during training. This problem known as Cover Source Mismatch (CSM) is particularly hard in realistic settings where practitioners (1) have access to only a small, unlabeled dataset, (2) are unsure of the processing techniques applied to these images, and (3) lack information on the proportion of covers and stegos in that set. To answer this challenge, we introduce TADA (Target Alignment through Data Adaptation), a framework learning to emulate the unknown processing pipeline from a small unlabeled target set. This architecture is trained with a loss combining residual covariance alignment, residual distribution matching, and a $\ell^2$ loss constraining the emulator to produce realistic images. Across toy and operational targets, TADA yields substantial gains in robustness to CSM and improves operational generalization compared to strong holistic and atomistic baselines. Additional resources are available at this link: https://github.com/RonyAbecidan/TADA

Milan Papež, Martin Rektoris, Tomáš Pevný et al.

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution over undirected cyclic graphs. This assumption of a generic graph structure brings various computational challenges, and, more importantly, the presence of non-linearities in neural networks does not permit tractable probabilistic inference. We address these problems by proposing sum-product-set networks, an extension of probabilistic circuits from unstructured tensor data to tree-structured graph data. To this end, we use random finite sets to reflect a variable number of nodes and edges in the graph and to allow for exact and efficient inference. We demonstrate that our tractable model performs comparably to various intractable models based on neural networks.

Leah Chrestien, Tomas Pevny, Antonin Komenda et al.

Optimization of heuristic functions for the A* algorithm, realized by deep neural networks, is usually done by minimizing square root loss of estimate of the cost to goal values. This paper argues that this does not necessarily lead to a faster search of A* algorithm since its execution relies on relative values instead of absolute ones. As a mitigation, we propose a L* loss, which upper-bounds the number of excessively expanded states inside the A* search. The L* loss, when used in the optimization of state-of-the-art deep neural networks for automated planning in maze domains like Sokoban and maze with teleports, significantly improves the fraction of solved problems, the quality of founded plans, and reduces the number of expanded states to approximately 50%

Milan Papež, Martin Rektoris, Václav Šmídl et al.

Deep generative models have recently made a remarkable progress in capturing complex probability distributions over graphs. However, they are intractable and thus unable to answer even the most basic probabilistic inference queries without resorting to approximations. Therefore, we propose graph sum-product networks (GraphSPNs), a tractable deep generative model which provides exact and efficient inference over (arbitrary parts of) graphs. We investigate different principles to make SPNs permutation invariant. We demonstrate that GraphSPNs are able to (conditionally) generate novel and chemically valid molecular graphs, being competitive to, and sometimes even better than, existing intractable models. We find out that (Graph)SPNs benefit from ensuring the permutation invariance via canonical ordering.

Simon Mandlik, Tomas Pevny, Vaclav Smidl et al.

Detection of malicious behavior in a large network is a challenging problem for machine learning in computer security, since it requires a model with high expressive power and scalable inference. Existing solutions struggle to achieve this feat -- current cybersec-tailored approaches are still limited in expressivity, and methods successful in other domains do not scale well for large volumes of data, rendering frequent retraining impossible. This work proposes a new perspective for learning from graph data that is modeling network entity interactions as a large heterogeneous graph. High expressivity of the method is achieved with neural network architecture HMILnet that naturally models this type of data and provides theoretical guarantees. The scalability is achieved by pursuing local graph inference, i.e., classifying individual vertices and their neighborhood as independent samples. Our experiments exhibit improvement over the state-of-the-art Probabilistic Threat Propagation (PTP) algorithm, show a further threefold accuracy improvement when additional data is used, which is not possible with the PTP algorithm, and demonstrate the generalization capabilities of the method to new, previously unseen entities.

Leah Chrestien, Tomás Pevný, Stefan Edelkamp et al.

In imitation learning for planning, parameters of heuristic functions are optimized against a set of solved problem instances. This work revisits the necessary and sufficient conditions of strictly optimally efficient heuristics for forward search algorithms, mainly A* and greedy best-first search, which expand only states on the returned optimal path. It then proposes a family of loss functions based on ranking tailored for a given variant of the forward search algorithm. Furthermore, from a learning theory point of view, it discusses why optimizing cost-to-goal \hstar\ is unnecessarily difficult. The experimental comparison on a diverse set of problems unequivocally supports the derived theory.

Tomáš Pevný, Viliam Lisý, Branislav Bošanský et al.

Learning from raw data input, thus limiting the need for feature engineering, is a component of many successful applications of machine learning methods in various domains. While many problems naturally translate into a vector representation directly usable in standard classifiers, a number of data sources have the natural form of structured data interchange formats (e.g., security logs in JSON/XML format). Existing methods, such as in Hierarchical Multiple Instance Learning (HMIL), allow learning from such data in their raw form. However, the explanation of the classifiers trained on raw structured data remains largely unexplored. By treating these models as sub-set selections problems, we demonstrate how interpretable explanations, with favourable properties, can be generated using computationally efficient algorithms. We compare to an explanation technique adopted from graph neural networks showing an order of magnitude speed-up and higher-quality explanations.

Jiri Nemecek, Tomas Pevny, Jakub Marecek

In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth of the tree and the accuracy in each leaf of the tree. We point out that decision trees containing leaves with unbalanced accuracy can provide misleading explanations. Low-accuracy leaves give less valid explanations, which could be interpreted as unfairness among subgroups utilizing these explanations. Here, we train a shallow tree with the objective of minimizing the maximum misclassification error across all leaf nodes. The shallow tree provides a global explanation, while the overall statistical performance of the shallow tree can become comparable to state-of-the-art methods (e.g., well-tuned XGBoost) by extending the leaves with further models.

Jiri Nemecek, Tomas Pevny, Jakub Marecek

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at https://github.com/Epanemu/LiCE.

Jaromír Janisch, Tomáš Pevný, Viliam Lisý

Current frameworks for training offensive penetration testing agents with deep reinforcement learning struggle to produce agents that perform well in real-world scenarios, due to the reality gap in simulation-based frameworks and the lack of scalability in emulation-based frameworks. Additionally, existing frameworks often use an unrealistic metric that measures the agents' performance on the training data. NASimEmu, a new framework introduced in this paper, addresses these issues by providing both a simulator and an emulator with a shared interface. This approach allows agents to be trained in simulation and deployed in the emulator, thus verifying the realism of the used abstraction. Our framework promotes the development of general agents that can transfer to novel scenarios unseen during their training. For the simulation part, we adopt an existing simulator NASim and enhance its realism. The emulator is implemented with industry-level tools, such as Vagrant, VirtualBox, and Metasploit. Experiments demonstrate that a simulation-trained agent can be deployed in emulation, and we show how to use the framework to train a general agent that transfers into novel, structurally different scenarios. NASimEmu is available as open-source.

Jiří Němeček, Mark Kozdoba, Illia Kryvoviaz et al.

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a distribution, to a given ground-truth reference dataset. However, classical metrics, such as the Total Variation and the Wasserstein distances, are known to have high sample complexities and, therefore, may fail to provide a meaningful distinction in many practical scenarios. In this paper, we propose a new notion of distance, the Maximum Subgroup Discrepancy (MSD). In this metric, two distributions are close if, roughly, discrepancies are low for all feature subgroups. While the number of subgroups may be exponential, we show that the sample complexity is linear in the number of features, thus making it feasible for practical applications. Moreover, we provide a practical algorithm for evaluating the distance based on Mixed-integer optimization (MIO). We also note that the proposed distance is easily interpretable, thus providing clearer paths to fixing the biases once they have been identified. Finally, we describe a natural general bias detection framework, termed MSDD distances, and show that MSD aligns well with this framework. We empirically evaluate MSD by comparing it with other metrics and by demonstrating the above properties of MSD on real-world datasets.

Armin Hadžić, Milan Papez, Tomáš Pevný

Deep generative models with discrete latent space, such as the Vector-Quantized Variational Autoencoder (VQ-VAE), offer excellent data generation capabilities, but, due to the large size of their latent space, their probabilistic inference is deemed intractable. We demonstrate that the VQ-VAE can be distilled into a tractable model by selecting a subset of latent variables with high probabilities. This simple strategy is particularly efficient, especially if the VQ-VAE underutilizes its latent space, which is, indeed, very often the case. We frame the distilled model as a probabilistic circuit, and show that it preserves expressiveness of the VQ-VAE while providing tractable probabilistic inference. Experiments illustrate competitive performance in density estimation and conditional generation tasks, challenging the view of the VQ-VAE as an inherently intractable model.

Martin Rektoris, Milan Papež, Václav Šmídl et al.

Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard probabilistic inference queries, i.e., these DGMs are considered \emph{intractable}. While recently proposed Probabilistic Graph Circuits (PGCs) address this issue by enabling \emph{tractable} probabilistic inference, they operate on dense graph representations with $\mathcal{O}(n^2)$ complexity for graphs with $n$ nodes and \emph{$m$ edges}. To address this scalability issue, we introduce Sparse PGCs, a new class of tractable generative models that operate directly on sparse graph representation, reducing the complexity to $\mathcal{O}(n + m)$, which is particularly beneficial for $m \ll n^2$. In the context of de novo drug design, we empirically demonstrate that SPGCs retain exact inference capabilities, improve memory efficiency and inference speed, and match the performance of intractable DGMs in key metrics.

Vít Škvára, Tomáš Pevný, Václav Šmídl

The area under receiver operating characteristics (AUC) is the standard measure for comparison of anomaly detectors. Its advantage is in providing a scalar number that allows a natural ordering and is independent on a threshold, which allows to postpone the choice. In this work, we question whether AUC is a good metric for anomaly detection, or if it gives a false sense of comfort, due to relying on assumptions which are unlikely to hold in practice. Our investigation shows that variations of AUC emphasizing accuracy at low false positive rate seem to be better correlated with the needs of practitioners, but also that we can compare anomaly detectors only in the case when we have representative examples of anomalous samples. This last result is disturbing, as it suggests that in many cases, we should do active or few-show learning instead of pure anomaly detection.

Leah Chrestien, Tomas Pevny, Antonin Komenda et al.

Learning a well-informed heuristic function for hard task planning domains is an elusive problem. Although there are known neural network architectures to represent such heuristic knowledge, it is not obvious what concrete information is learned and whether techniques aimed at understanding the structure help in improving the quality of the heuristics. This paper presents a network model to learn a heuristic capable of relating distant parts of the state space via optimal plan imitation using the attention mechanism, which drastically improves the learning of a good heuristic function. To counter the limitation of the method in the creation of problems of increasing difficulty, we demonstrate the use of curriculum learning, where newly solved problem instances are added to the training set, which, in turn, helps to solve problems of higher complexities and far exceeds the performances of all existing baselines including classical planning heuristics. We demonstrate its effectiveness for grid-type PDDL domains.

Milan Papež, Tomáš Pevný, Václav Šmídl

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for example, in the sum-product (transform) networks. Therefore, we propose to apply a combination of the expectation maximization and the Metropolis-Hastings algorithm to evaluate only a small number of, stochastically sampled, components, thus substantially reducing the computational cost. The Markov chain of component assignments is sequentially generated across the algorithm's iterations, having a non-stationary target distribution whose parameters vary via a gradient-descent scheme. We put emphasis on generality of our method, equipping it with the ability to train both shallow and deep mixture models which involve complex, and possibly nonlinear, transformations. The performance of our method is illustrated in a variety of synthetic and real-data contexts, considering deep models, such as mixtures of normalizing flows and sum-product (transform) networks.

Maximilian Samsinger, Florian Merkle, Pascal Schöttle et al.

Adversarial machine learning, i.e., increasing the robustness of machine learning algorithms against so-called adversarial examples, is now an established field. Yet, newly proposed methods are evaluated and compared under unrealistic scenarios where costs for adversary and defender are not considered and either all samples or no samples are adversarially perturbed. We scrutinize these assumptions and propose the advanced adversarial classification game, which incorporates all relevant parameters of an adversary and a defender. Especially, we take into account economic factors on both sides and the fact that all so far proposed countermeasures against adversarial examples reduce accuracy on benign samples. Analyzing the scenario in detail, where both players have two pure strategies, we identify all best responses and conclude that in practical settings, the most influential factor might be the maximum amount of adversarial examples.

Simon Mandlik, Matej Racinsky, Viliam Lisy et al.

Learning from raw data input, thus limiting the need for manual feature engineering, is one of the key components of many successful applications of machine learning methods. While machine learning problems are often formulated on data that naturally translate into a vector representation suitable for classifiers, there are data sources, for example in cybersecurity, that are naturally represented in diverse files with a unifying hierarchical structure, such as XML, JSON, and Protocol Buffers. Converting this data to vector (tensor) representation is generally done by manual feature engineering, which is laborious, lossy, and prone to human bias about the importance of particular features. Mill and JsonGrinder is a tandem of libraries, which fully automates the conversion. Starting with an arbitrary set of JSON samples, they create a differentiable machine learning model capable of infer from further JSON samples in their raw form.

Simon Mandlik, Tomas Pevny

Even though machine learning algorithms already play a significant role in data science, many current methods pose unrealistic assumptions on input data. The application of such methods is difficult due to incompatible data formats, or heterogeneous, hierarchical or entirely missing data fragments in the dataset. As a solution, we propose a versatile, unified framework called `HMill' for sample representation, model definition and training. We review in depth a multi-instance paradigm for machine learning that the framework builds on and extends. To theoretically justify the design of key components of HMill, we show an extension of the universal approximation theorem to the set of all functions realized by models implemented in the framework. The text also contains a detailed discussion on technicalities and performance improvements in our implementation, which is published for download under the MIT License. The main asset of the framework is its flexibility, which makes modelling of diverse real-world data sources with the same tool possible. Additionally to the standard setting in which a set of attributes is observed for each object individually, we explain how message-passing inference in graphs that represent whole systems of objects can be implemented in the framework. To support our claims, we solve three different problems from the cybersecurity domain using the framework. The first use case concerns IoT device identification from raw network observations. In the second problem, we study how malicious binary files can be classified using a snapshot of the operating system represented as a directed graph. The last provided example is a task of domain blacklist extension through modelling interactions between entities in the network. In all three problems, the solution based on the proposed framework achieves performance comparable to specialized approaches.

Vít Škvára, Jan Franců, Matěj Zorek et al.

Deep generative models are challenging the classical methods in the field of anomaly detection nowadays. Every new method provides evidence of outperforming its predecessors, often with contradictory results. The objective of this comparison is twofold: to compare anomaly detection methods of various paradigms with focus on deep generative models, and identification of sources of variability that can yield different results. The methods were compared on popular tabular and image datasets. We identified the main sources of variability to be experimental conditions: i) the type data set (tabular or image) and the nature of anomalies (statistical or semantic), and ii) strategy of selection of hyperparameters, especially the number of available anomalies in the validation set. Different methods perform the best in different contexts, i.e. combination of experimental conditions together with computational time. This explains the variability of the previous results and highlights the importance of careful specification of the context in the publication of a new method. All our code and results are available for download.

Jaromír Janisch, Tomáš Pevný, Viliam Lisý

We focus on reinforcement learning (RL) in relational problems that are naturally defined in terms of objects, their relations, and object-centric actions. These problems are characterized by variable state and action spaces, and finding a fixed-length representation, required by most existing RL methods, is difficult, if not impossible. We present a deep RL framework based on graph neural networks and auto-regressive policy decomposition that naturally works with these problems and is completely domain-independent. We demonstrate the framework's broad applicability in three distinct domains and show impressive zero-shot generalization over different problem sizes.

Niklas Heim, Tomáš Pevný, Václav Šmídl

Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic units are either limited to operate on positive numbers or can only represent a subset of arithmetic operations. We introduce the Neural Power Unit (NPU) that operates on the full domain of real numbers and is capable of learning arbitrary power functions in a single layer. The NPU thus fixes the shortcomings of existing arithmetic units and extends their expressivity. We achieve this by using complex arithmetic without requiring a conversion of the network to complex numbers. A simplification of the unit to the RealNPU yields a highly transparent model. We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.

Tomas Pevny, Vasek Smidl, Martin Trapp et al.

In this work, we propose Sum-Product-Transform Networks (SPTN), an extension of sum-product networks that uses invertible transformations as additional internal nodes. The type and placement of transformations determine properties of the resulting SPTN with many interesting special cases. Importantly, SPTN with Gaussian leaves and affine transformations pose the same inference task tractable that can be computed efficiently in SPNs. We propose to store affine transformations in their SVD decompositions using an efficient parametrization of unitary matrices by a set of Givens rotations. Last but not least, we demonstrate that G-SPTNs achieve state-of-the-art results on the density estimation task and are competitive with state-of-the-art methods for anomaly detection.

Lukáš Adam, Václav Mácha, Václav Šmídl et al.

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework to handle these classes of problems and show which known methods (both known and newly proposed) fall into this framework. We provide a theoretical analysis of this framework and mention selected possible pitfalls the methods may encounter. We suggest several numerical improvements including the implicit derivative and stochastic gradient descent. We provide an extensive numerical study. Based both on the theoretical properties and numerical experiments, we conclude the paper by suggesting which method should be used in which situation.

Tomas Pevny, Marek Dedic

In many interesting cases, the application of machine learning is hindered by data having a complicated structure stimulated by a structured file-formats like JSONs, XMLs, or ProtoBuffers, which is non-trivial to convert to a vector / matrix. Moreover, since the structure frequently carries a semantic meaning, reflecting it in the machine learning model should improve the accuracy but more importantly it facilitates the explanation of decisions and the model. This paper demonstrates on the identification of infected computers in the computer network from their HTTP traffic, how to achieve this reflection using recent progress in multiple-instance learning. The proposed model is compared to complementary approaches from the prior art, the first relying on human-designed features and the second on automatically learned features through convolution neural networks. In a challenging scenario measuring accuracy only on unseen domains/malware families, the proposed model is superior to the prior art while providing a valuable feedback to the security researchers. We believe that the proposed framework will found applications elsewhere even beyond the field of security.

Niklas Heim, Václav Šmídl, Tomáš Pevný

We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural Arithmetic Units. For maximal explainability of the learnt model, we minimise the state size of the ODE as well as the number of non-zero parameters that are needed to solve the problem. This sparsification is realized through a combination of the Variational Auto-Encoder (VAE) and Automatic Relevance Determination (ARD). We show that it is possible to learn not only one specific model for a single process, but a manifold of models representing harmonic signals as well as a manifold of Lotka-Volterra systems.

Jaromír Janisch, Tomáš Pevný, Viliam Lisý

Classification with Costly Features (CwCF) is a classification problem that includes the cost of features in the optimization criteria. Individually for each sample, its features are sequentially acquired to maximize accuracy while minimizing the acquired features' cost. However, existing approaches can only process data that can be expressed as vectors of fixed length. In real life, the data often possesses rich and complex structure, which can be more precisely described with formats such as XML or JSON. The data is hierarchical and often contains nested lists of objects. In this work, we extend an existing deep reinforcement learning-based algorithm with hierarchical deep sets and hierarchical softmax, so that it can directly process this data. The extended method has greater control over which features it can acquire and, in experiments with seven datasets, we show that this leads to superior performance. To showcase the real usage of the new method, we apply it to a real-life problem of classifying malicious web domains, using an online service.

Jaromír Janisch, Tomáš Pevný, Viliam Lisý

This work focuses on a specific classification problem, where the information about a sample is not readily available, but has to be acquired for a cost, and there is a per-sample budget. Inspired by real-world use-cases, we analyze average and hard variations of a directly specified budget. We postulate the problem in its explicit formulation and then convert it into an equivalent MDP, that can be solved with deep reinforcement learning. Also, we evaluate a real-world inspired setting with sparse training dataset with missing features. The presented method performs robustly well in all settings across several distinct datasets, outperforming other prior-art algorithms. The method is flexible, as showcased with all mentioned modifications and can be improved with any domain independent advancement in RL.

Paul Prasse, Rene Knaebel, Lukas Machlica et al.

Detection of malware-infected computers and detection of malicious web domains based on their encrypted HTTPS traffic are challenging problems, because only addresses, timestamps, and data volumes are observable. The detection problems are coupled, because infected clients tend to interact with malicious domains. Traffic data can be collected at a large scale, and antivirus tools can be used to identify infected clients in retrospect. Domains, by contrast, have to be labeled individually after forensic analysis. We explore transfer learning based on sluice networks; this allows the detection models to bootstrap each other. In a large-scale experimental study, we find that the model outperforms known reference models and detects previously unknown malware, previously unknown malware families, and previously unknown malicious domains.

Tomas Pevny, Vojtech Kovarik

This paper extends the proof of density of neural networks in the space of continuous (or even measurable) functions on Euclidean spaces to functions on compact sets of probability measures. By doing so the work parallels a more then a decade old results on mean-map embedding of probability measures in reproducing kernel Hilbert spaces. The work has wide practical consequences for multi-instance learning, where it theoretically justifies some recently proposed constructions. The result is then extended to Cartesian products, yielding universal approximation theorem for tree-structured domains, which naturally occur in data-exchange formats like JSON, XML, YAML, AVRO, and ProtoBuffer. This has important practical implications, as it enables to automatically create an architecture of neural networks for processing structured data (AutoML paradigms), as demonstrated by an accompanied library for JSON format.

Václav Šmídl, Jan Bím, Tomáš Pevný

Reconstruction error is a prevalent score used to identify anomalous samples when data are modeled by generative models, such as (variational) auto-encoders or generative adversarial networks. This score relies on the assumption that normal samples are located on a manifold and all anomalous samples are located outside. Since the manifold can be learned only where the training data lie, there are no guarantees how the reconstruction error behaves elsewhere and the score, therefore, seems to be ill-defined. This work defines an anomaly score that is theoretically compatible with generative models, and very natural for (variational) auto-encoders as they seem to be prevalent. The new score can be also used to select hyper-parameters and models. Finally, we explain why reconstruction error delivers good experimental results despite weak theoretical justification.

Vít Škvára, Tomáš Pevný, Václav Šmídl

Many deep models have been recently proposed for anomaly detection. This paper presents comparison of selected generative deep models and classical anomaly detection methods on an extensive number of non--image benchmark datasets. We provide statistical comparison of the selected models, in many configurations, architectures and hyperparamaters. We arrive to conclusion that performance of the generative models is determined by the process of selection of their hyperparameters. Specifically, performance of the deep generative models deteriorates with decreasing amount of anomalous samples used in hyperparameter selection. In practical scenarios of anomaly detection, none of the deep generative models systematically outperforms the kNN.

Vyacheslav Kungurtsev, Tomas Pevny

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonconvex. This alone presents a challenge to application and development of appropriate optimization algorithms for solving the problem. However, in addition, there are a number of interesting problems for which the objective function is non- smooth and nonseparable. In this paper, we summarize the primary challenges involved, the state of the art, and present some numerical results on an interesting and representative class of problems.

Vyacheslav Kungurtsev, Tomas Pevny

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonlinear. This presents a challenge to application and development of appropriate optimization algorithms for solving the problem. In this paper, we summarize the primary challenges involved and present the case for a Newton-based method incorporating directions of negative curvature, including promising numerical results on data arising from security anomally deetection.

Jaromír Janisch, Tomáš Pevný, Viliam Lisý

We study a classification problem where each feature can be acquired for a cost and the goal is to optimize a trade-off between the expected classification error and the feature cost. We revisit a former approach that has framed the problem as a sequential decision-making problem and solved it by Q-learning with a linear approximation, where individual actions are either requests for feature values or terminate the episode by providing a classification decision. On a set of eight problems, we demonstrate that by replacing the linear approximation with neural networks the approach becomes comparable to the state-of-the-art algorithms developed specifically for this problem. The approach is flexible, as it can be improved with any new reinforcement learning enhancement, it allows inclusion of pre-trained high-performance classifier, and unlike prior art, its performance is robust across all evaluated datasets.

Jan Stiborek, Tomáš Pevný, Martin Rehák

This work addresses classification of unknown binaries executed in sandbox by modeling their interaction with system resources (files, mutexes, registry keys and communication with servers over the network) and error messages provided by the operating system, using vocabulary-based method from the multiple instance learning paradigm. It introduces similarities suitable for individual resource types that combined with an approximative clustering method efficiently group the system resources and define features directly from data. This approach effectively removes randomization often employed by malware authors and projects samples into low-dimensional feature space suitable for common classifiers. An extensive comparison to the state of the art on a large corpus of binaries demonstrates that the proposed solution achieves superior results using only a fraction of training samples. Moreover, it makes use of a source of information different than most of the prior art, which increases the diversity of tools detecting the malware, hence making detection evasion more difficult.

Tomas Pevny, Petr Somol

Modeling network traffic is gaining importance in order to counter modern threats of ever increasing sophistication. It is though surprisingly difficult and costly to construct reliable classifiers on top of telemetry data due to the variety and complexity of signals that no human can manage to interpret in full. Obtaining training data with sufficiently large and variable body of labels can thus be seen as prohibitive problem. The goal of this work is to detect infected computers by observing their HTTP(S) traffic collected from network sensors, which are typically proxy servers or network firewalls, while relying on only minimal human input in model training phase. We propose a discriminative model that makes decisions based on all computer's traffic observed during predefined time window (5 minutes in our case). The model is trained on collected traffic samples over equally sized time window per large number of computers, where the only labels needed are human verdicts about the computer as a whole (presumed infected vs. presumed clean). As part of training the model itself recognizes discriminative patterns in traffic targeted to individual servers and constructs the final high-level classifier on top of them. We show the classifier to perform with very high precision, while the learned traffic patterns can be interpreted as Indicators of Compromise. In the following we implement the discriminative model as a neural network with special structure reflecting two stacked multi-instance problems. The main advantages of the proposed configuration include not only improved accuracy and ability to learn from gross labels, but also automatic learning of server types (together with their detectors) which are typically visited by infected computers.

Tomas Pevny, Petr Somol

Many objects in the real world are difficult to describe by a single numerical vector of a fixed length, whereas describing them by a set of vectors is more natural. Therefore, Multiple instance learning (MIL) techniques have been constantly gaining on importance throughout last years. MIL formalism represents each object (sample) by a set (bag) of feature vectors (instances) of fixed length where knowledge about objects (e.g., class label) is available on bag level but not necessarily on instance level. Many standard tools including supervised classifiers have been already adapted to MIL setting since the problem got formalized in late nineties. In this work we propose a neural network (NN) based formalism that intuitively bridges the gap between MIL problem definition and the vast existing knowledge-base of standard models and classifiers. We show that the proposed NN formalism is effectively optimizable by a modified back-propagation algorithm and can reveal unknown patterns inside bags. Comparison to eight types of classifiers from the prior art on a set of 14 publicly available benchmark datasets confirms the advantages and accuracy of the proposed solution.