In this paper, we study the problem of constrained robust (min-max) optimization ina black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an alternating projected stochastic gradient descent-ascent method, where the former only requires a small number of function queries and the later needs just one-step descent/ascent update. We show that the proposed framework, referred to as ZO-Min-Max, has a sub-linear convergence rate under mild conditions and scales gracefully with problem size. From an application side, we explore a promising connection between black-box min-max optimization and black-box evasion and poisoning attacks in adversarial machine learning (ML). Our empirical evaluations on these use cases demonstrate the effectiveness of our approach and its scalability to dimensions that prohibit using recent black-box solvers.

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks. In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions. Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time and even speed up or slow down the learned dynamics. We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities. We hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to deep learning.

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt, as well as how the addition of symmetry invariance constraints can improve data efficiency and generalisation. Finally, we make connections to disentangled representation learning and show how this work relates to a recently proposed definition.

Nowadays processing of Big Security Data, such as log messages, is commonly used for intrusion detection purposed. Its heterogeneous nature, as well as combination of numerical and categorical attributes does not allow to apply the existing data mining methods directly on the data without feature preprocessing. Therefore, a rather computationally expensive conversion of categorical attributes into vector space should be utilised for analysis of such data. However, a well-known k-modes algorithm allows to cluster the categorical data directly and avoid conversion into the vector space. The existing implementations of k-modes for Big Data processing are ensemble-based and utilise two-step clustering, where data subsets are first clustered independently, whereas the resulting cluster modes are clustered again in order to calculate metamodes valid for all data subsets. In this paper, the novel frequency-based distance function is proposed for the second step of ensemble-based k-modes clustering. Besides this, the existing feature discretisation method from the previous work is utilised in order to adapt k-modes for processing of mixed data sets. The resulting k-metamodes algorithm was tested on two public security data sets and reached higher effectiveness in comparison with the previous work.

We propose Nonlinear Dipole Inversion (NDI) for high - quality Quantitative Susceptibility Mapping (QSM) without regularization tuning, while matching the image quality of state - of - the - art reconstruction techniques. In addition to avoiding over - smoothing that these techniques often suffer from, we also ob viate the need for parameter selection. NDI is flexible enough to allow for reconstruction from an arbitrary number of head orientations, and outperforms COSMOS even when using as few as 1 - direction data . This is made possible by a nonlinear forward - model that uses the magnitude as an effective prior, for which we derived a simple gradient descent update rule . We synergistically combine this physics - model with a Variational Network (VN) to leverage the power of d eep l earning in the VaNDI algorithm. This technique adopts the simple gradient descent rule from NDI and learns the network parameters during training, hence requires no additional parameter tuning. Further, we evaluate NDI at 7T using highly accelerated Wave - CAIPI acquisition s at 0.5 mm isotropic resolutio n and demonstrate high - quality QSM from as f e w as 2 - direction data .

Bayesian optimization (BO) is a popular methodology to tune the hyperparameters of expensive black-box functions. Despite its success, standard BO focuses on a single task at a time and is not designed to leverage information from related functions, such as tuning performance metrics of the same algorithm across multiple datasets. In this work, we introduce a novel approach to achieve transfer learning across different datasets as well as different metrics. The main idea is to regress the mapping from hyperparameter to metric quantiles with a semi-parametric Gaussian Copula distribution, which provides robustness against different scales or outliers that can occur in different tasks. We introduce two methods to leverage this estimation: a Thompson sampling strategy as well as a Gaussian Copula process using such quantile estimate as a prior. We show that these strategies can combine the estimation of multiple metrics such as runtime and accuracy, steering the optimization toward cheaper hyperparameters for the same level of accuracy. Experiments on an extensive set of hyperparameter tuning tasks demonstrate significant improvements over state-of-the-art methods.

A BSTRACT In this paper we investigate an artificial agent's ability to perform task-focused tool synthesis via imagination. Our motivation is to explore the richness of information captured by the latent space of an object-centric generative model - and how to exploit it. In particular, our approach employs activation maximisation of a task-based performance predictor to optimise the latent variable of a structured latent-space model in order to generate tool geometries appropriate for the task at hand. We evaluate our model using a novel dataset of synthetic reaching tasks inspired by the cognitive sciences and behavioural ecology. In doing so we examine the model's ability to imagine tools for increasingly complex scenario types, beyond those seen during training. Our experiments demonstrate that the synthesis process modifies emergent, task-relevant object affordances in a targeted and deliberate way: the agents often specifically modify aspects of the tools which relate to meaningful (yet implicitly learned) concepts such as a tool's length, width and configuration. Our results therefore suggest that task relevant object affordances are implicitly encoded as directions in a structured latent space shaped by experience. 1 I NTRODUCTION Deep generative models are gaining in popularity for unsupervised representation learning. In particular, recent models like MONet (Burgess et al., 2019) have been proposed to decompose scenes into object-centric latent representations (cf. The notion of such an object-centric latent representation, trained from examples in an unsupervised way, holds a tantalising prospect: as generative models naturally capture factors of variation, could they also be used to expose these factors such that they can be modified in a task-driven way? We posit that a task-driven traversal of a structured latent space leads to affordances emerging naturally as directions in this space. This is in stark contrast to more common approaches to affordance learning where it is commonly achieved via direct supervision or implicitly via imitation (e.g. Tikhanoff et al., 2013; Myers et al., 2015; Liu et al., 2018; Grabner et al., 2011; Do et al., 2018).

Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow (GRF). The GRF is based on residual flows, which are known for more flexible and complex non-linear mappings than traditional coupling flows. We theoretically derive non-trivial conditions such that GRF is invertible, and present a way of keeping the entire flows invertible throughout the training and sampling. Experimental results show that a generative model based on the proposed GRF achieves comparable generation performance, with much smaller number of trainable parameters compared to the existing flow-based model.

Modern data sets in many applications no longer comprise samples of real vectors in a real vector space but samples of much more complex structures which may be represented as points in a space with certain underlying geometric structure, namely a manifold. Manifold learning is an emerging field for learning the underlying structure. The study of manifold learning can be split into two main branches, namely dimension reduction and manifold fitting. With the aim of interacting statistics and geometry, we tackle the problem of manifold fitting in the ambient space. Inspired by the relation between the eigenvalues of the Laplace-Beltrami operator and the geometry of a manifold, we aim to find a small set of points that preserve the geometry of the underlying manifold. Based on this relationship, we extend the idea of subsampling to noisy datasets in high dimensional space and utilize the Moving Least Squares (MLS) approach to approximate the underlying manifold. We analyze the two core steps in our proposed method theoretically and also provide the bounds for the MLS approach. Our simulation results and real data analysis demonstrate the superiority of our method in estimating the underlying manifold from noisy data.

The performance of many network learning applications crucially hinges on the success of network embedding algorithms, which aim to encode rich network information into low-dimensional vertex-based vector representations. This paper considers a novel variational formulation of network embeddings, with special focus on textual networks. Different from most existing methods that optimize a discriminative objective, we introduce Variational Homophilic Embedding (VHE), a fully generative model that learns network embeddings by modeling the semantic (textual) information with a variational autoencoder, while accounting for the structural (topology) information through a novel homophilic prior design. Homophilic vertex embeddings encourage similar embedding vectors for related (connected) vertices. The proposed VHE promises better generalization for downstream tasks, robustness to incomplete observations, and the ability to generalize to unseen vertices. Extensive experiments on real-world networks, for multiple tasks, demonstrate that the proposed method consistently achieves superior performance relative to competing state-of-the-art approaches.