Deep Learning of Conjugate Mappings

Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincar\'e first made this connection by tracking consecutive iterations of the continuous flow with a lower-dimensional, transverse subspace. The mapping that iterates the dynamics through consecutive intersections of the flow with the subspace is now referred to as a Poincar\'e map, and it is the primary method available for interpreting and classifying chaotic dynamics. Unfortunately, in all but the simplest systems, an explicit form for such a mapping remains outstanding. This work proposes a method for obtaining explicit Poincar\'e mappings by using deep learning to construct an invertible coordinate transformation into a conjugate representation where the dynamics are governed by a relatively simple chaotic mapping. The invertible change of variable is based on an autoencoder, which allows for dimensionality reduction, and has the advantage of classifying chaotic systems using the equivalence relation of topological conjugacies. Indeed, the enforcement of topological conjugacies is the critical neural network regularization for learning the coordinate and dynamics pairing. We provide expository applications of the method to low-dimensional systems such as the R\"ossler and Lorenz systems, while also demonstrating the utility of the method on infinite-dimensional systems, such as the Kuramoto--Sivashinsky equation.

Locally Differentially Private Federated Learning: Efficient Algorithms with Tight Risk Bounds

Federated learning (FL) is a distributed learning paradigm in which many clients with heterogeneous, unbalanced, and often sensitive local data, collaborate to learn a model. Local Differential Privacy (LDP) provides a strong guarantee that each client's data cannot be leaked during and after training, without relying on a trusted third party. While LDP is often believed to be too stringent to allow for satisfactory utility, our paper challenges this belief. We consider a general setup with unbalanced, heterogeneous data, disparate privacy needs across clients, and unreliable communication, where a random number/subset of clients is available each round. We propose three LDP algorithms for smooth (strongly) convex FL; each are noisy variations of distributed minibatch SGD. One is accelerated and one involves novel time-varying noise, which we use to obtain the first non-trivial LDP excess risk bound for the fully general non-i.i.d. FL problem. Specializing to i.i.d. clients, our risk bounds interpolate between the best known and/or optimal bounds in the centralized setting and the cross-device setting, where each client represents just one person's data. Furthermore, we show that in certain regimes, our convergence rate (nearly) matches the corresponding non-private lower bound or outperforms state of the art non-private algorithms (``privacy for free''). Finally, we validate our theoretical results and illustrate the practical utility of our algorithm with numerical experiments.

Navigation Turing Test (NTT): Learning to Evaluate Human-Like Navigation

A key challenge on the path to developing agents that learn complex human-like behavior is the need to quickly and accurately quantify human-likeness. While human assessments of such behavior can be highly accurate, speed and scalability are limited. We address these limitations through a novel automated Navigation Turing Test (ANTT) that learns to predict human judgments of human-likeness. We demonstrate the effectiveness of our automated NTT on a navigation task in a complex 3D environment. We investigate six classification models to shed light on the types of architectures best suited to this task, and validate them against data collected through a human NTT. Our best models achieve high accuracy when distinguishing true human and agent behavior. At the same time, we show that predicting finer-grained human assessment of agents' progress towards human-like behavior remains unsolved. Our work takes an important step towards agents that more effectively learn complex human-like behavior.

Nonlinear Hawkes Process with Gaussian Process Self Effects

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes. Efficient approximate Bayesian inference is achieved via data augmentation, and we describe a mean--field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from three different domains and compare it to previously reported results.

Adversarial training in communication constrained federated learning

Federated learning enables model training over a distributed corpus of agent data. However, the trained model is vulnerable to adversarial examples, designed to elicit misclassification. We study the feasibility of using adversarial training (AT) in the federated learning setting. Furthermore, we do so assuming a fixed communication budget and non-iid data distribution between participating agents. We observe a significant drop in both natural and adversarial accuracies when AT is used in the federated setting as opposed to centralized training. We attribute this to the number of epochs of AT performed locally at the agents, which in turn effects (i) drift between local models; and (ii) convergence time (measured in number of communication rounds). Towards this end, we propose FedDynAT, a novel algorithm for performing AT in federated setting. Through extensive experimentation we show that FedDynAT significantly improves both natural and adversarial accuracy, as well as model convergence time by reducing the model drift.

Automated Generation of Robotic Planning Domains from Observations

Automated planning enables robots to find plans to achieve complex, long-horizon tasks, given a planning domain. This planning domain consists of a list of actions, with their associated preconditions and effects, and is usually manually defined by a human expert, which is very time-consuming or even infeasible. In this paper, we introduce a novel method for generating this domain automatically from human demonstrations. First, we automatically segment and recognize the different observed actions from human demonstrations. From these demonstrations, the relevant preconditions and effects are obtained, and the associated planning operators are generated. Finally, a sequence of actions that satisfies a user-defined goal can be planned using a symbolic planner. The generated plan is executed in a simulated environment by the TIAGo robot. We tested our method on a dataset of 12 demonstrations collected from three different participants. The results show that our method is able to generate executable plans from using one single demonstration with a 92% success rate, and 100% when the information from all demonstrations are included, even for previously unknown stacking goals.

A Consistent Method for Learning OOMs from Asymptotically Stationary Time Series Data Containing Missing Values

In the traditional framework of spectral learning of stochastic time series models, model parameters are estimated based on trajectories of fully recorded observations. However, real-world time series data often contain missing values, and worse, the distributions of missingness events over time are often not independent of the visible process. Recently, a spectral OOM learning algorithm for time series with missing data was introduced and proved to be consistent, albeit under quite strong conditions. Here we refine the algorithm and prove that the original strong conditions can be very much relaxed. We validate our theoretical findings by numerical experiments, showing that the algorithm can consistently handle missingness patterns whose dynamic interacts with the visible process.

Dynamic Graph-Based Anomaly Detection in the Electrical Grid

Given sensor readings over time from a power grid, how can we accurately detect when an anomaly occurs? A key part of achieving this goal is to use the network of power grid sensors to quickly detect, in real-time, when any unusual events, whether natural faults or malicious, occur on the power grid. Existing bad-data detectors in the industry lack the sophistication to robustly detect broad types of anomalies, especially those due to emerging cyber-attacks, since they operate on a single measurement snapshot of the grid at a time. New ML methods are more widely applicable, but generally do not consider the impact of topology change on sensor measurements and thus cannot accommodate regular topology adjustments in historical data. Hence, we propose DYNWATCH, a domain knowledge based and topology-aware algorithm for anomaly detection using sensors placed on a dynamic grid. Our approach is accurate, outperforming existing approaches by 20% or more (F-measure) in experiments; and fast, running in less than 1.7ms on average per time tick per sensor on a 60K+ branch case using a laptop computer, and scaling linearly in the size of the graph.

A Comprehensive Review of Image Analysis Methods for Microorganism Counting: From Classical Image Processing to Deep Learning Approaches

Microorganisms such as bacteria and fungi play essential roles in many application fields, like biotechnique, medical technique and industrial domain. Microorganism counting techniques are crucial in microorganism analysis, helping biologists and related researchers quantitatively analyze the microorganisms and calculate their characteristics, such as biomass concentration and biological activity. However, traditional microorganism manual counting methods are time consuming and subjective, which cannot be applied in large-scale applications. In order to improve this situation, image analysis-based microorganism counting systems are developed since 1980s, which consists of digital image processing, image segmentation, image classification and so on. Moreover, image analysis-based microorganism counting methods are efficient comparing with traditional plate counting methods. In this article, we have studied the development of microorganism counting methods using digital image analysis. Firstly, the microorganisms are grouped as bacteria and other microorganisms. Then, the related articles are summarized based on image segmentation methods. Each part of articles are reviewed by time periods. Moreover, commonly used image processing methods for microorganism counting are summarized and analyzed to find technological common points. More than 142 papers are summarized in this article. In conclusion, this article can be referred to researchers to determine the development trend in microorganism counting field and further analyze the potential applications

Manipulating SGD with Data Ordering Attacks

Machine learning is vulnerable to a wide variety of different attacks. It is now well understood that by changing the underlying data distribution, an adversary can poison the model trained with it or introduce backdoors. In this paper we present a novel class of training-time attacks that require no changes to the underlying model dataset or architecture, but instead only change the order in which data are supplied to the model. In particular, an attacker can disrupt the integrity and availability of a model by simply reordering training batches, with no knowledge about either the model or the dataset. Indeed, the attacks presented here are not specific to the model or dataset, but rather target the stochastic nature of modern learning procedures. We extensively evaluate our attacks to find that the adversary can disrupt model training and even introduce backdoors. For integrity we find that the attacker can either stop the model from learning, or poison it to learn behaviours specified by the attacker. For availability we find that a single adversarially-ordered epoch can be enough to slow down model learning, or even to reset all of the learning progress. Such attacks have a long-term impact in that they decrease model performance hundreds of epochs after the attack took place. Reordering is a very powerful adversarial paradigm in that it removes the assumption that an adversary must inject adversarial data points or perturbations to perform training-time attacks. It reminds us that stochastic gradient descent relies on the assumption that data are sampled at random. If this randomness is compromised, then all bets are off.