We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of tree-structured Ising models. Without any additional assumption of side information, this is an open problem. We first prove that this problem is unidentifiable, however, this unidentifiability is limited to a small equivalence class of trees formed by leaf nodes exchanging positions with their neighbors. Next, we propose an algorithm to solve the above problem with logarithmic sample complexity in the number of nodes and polynomial run-time complexity. Lastly, we empirically demonstrate that, as expected, existing algorithms are not inherently robust in the proposed setting whereas our algorithm correctly recovers the underlying equivalence class.

Discovering causal structure among a set of variables is a fundamental problem in many domains. However, state-of-the-art methods seldom consider the possibility that the observational data has missing values (incomplete data), which is ubiquitous in many real-world situations. The missing value will significantly impair the performance and even make the causal discovery algorithms fail. In this paper, we propose an approach to discover causal structures from incomplete data by using a novel encoder and reinforcement learning (RL). The encoder is designed for missing data imputation as well as feature extraction. In particular, it learns to encode the currently available information (with missing values) into a robust feature representation which is then used to determine where to search the best graph. The encoder is integrated into a RL framework that can be optimized using the actor-critic algorithm. Our method takes the incomplete observational data as input and generates a causal structure graph. Experimental results on synthetic and real data demonstrate that our method can robustly generate causal structures from incomplete data. Compared with the direct combination of data imputation and causal discovery methods, our method performs generally better and can even obtain a performance gain as much as 43.2%.

Learning theory mostly addresses the standard learning paradigm, assuming the availability of complete and correct supervision signals for large amounts of data. However, in practice, machine learning researchers and practitioners acquire and make use of a range of {\em incidental supervision} signals that only have statistical associations with the gold supervision. This paper addresses the question: {\em Can one quantify models' performance when learning with such supervision signals, without going through an exhaustive experimentation process with various supervision signals and learning protocols?} To quantify the benefits of various incidental supervision signals, we propose a unified PAC-Bayesian Informativeness measure (PABI), characterizing the reduction in uncertainty that incidental supervision signals provide. We then demonstrate PABI's use in quantifying various types of incidental signals such as partial labels, noisy labels, constraints, cross-domain signals, and some combinations of these. Experiments on named entity recognition and question answering show that PABI correlates well with learning performance, providing a promising way to determine, ahead of learning, which supervision signals would be beneficial.

Small disturbances can trigger functional breakdowns in complex systems. A challenging task is to infer the structural cause of a disturbance in a networked system, soon enough to prevent a catastrophe. We present a graph neural network approach, borrowed from the deep learning paradigm, to infer structural perturbations from functional time series. We show our data-driven approach outperforms typical reconstruction methods while meeting the accuracy of Bayesian inference. We validate the versatility and performance of our approach with epidemic spreading, population dynamics, and neural dynamics, on various network structures: random networks, scale-free networks, 25 real food-web systems, and the C. Elegans connectome. Moreover, we report that our approach is robust to data corruption. This work uncovers a practical avenue to study the resilience of real-world complex systems.

We study a contextual bandit setting where the learning agent has access to sampled bandit instances from an unknown prior distribution $\mathcal{P}$. The goal of the agent is to achieve high reward on average over the instances drawn from $\mathcal{P}$. This setting is of a particular importance because it formalizes the offline optimization of bandit policies, to perform well on average over anticipated bandit instances. The main idea in our work is to optimize differentiable bandit policies by policy gradients. We derive reward gradients that reflect the structure of our problem, and propose contextual policies that are parameterized in a differentiable way and have low regret. Our algorithmic and theoretical contributions are supported by extensive experiments that show the importance of baseline subtraction, learned biases, and the practicality of our approach on a range of classification tasks.

We present CRISP (COVID-19 Risk Score Prediction), a probabilistic graphical model for COVID-19 infection spread through a population based on the SEIR model where we assume access to (1) mutual contacts between pairs of individuals across time across various channels (e.g., Bluetooth contact traces), as well as (2) test outcomes at given times for infection, exposure and immunity tests. Our micro-level model keeps track of the infection state for each individual at every point in time, ranging from susceptible, exposed, infectious to recovered. We develop a Monte Carlo EM algorithm to infer contact-channel specific infection transmission probabilities. Our algorithm uses Gibbs sampling to draw samples of the latent infection status of each individual over the entire time period of analysis, given the latent infection status of all contacts and test outcome data. Experimental results with simulated data demonstrate our CRISP model can be parametrized by the reproduction factor $R_0$ and exhibits population-level infectiousness and recovery time series similar to those of the classical SEIR model. However, due to the individual contact data, this model allows fine grained control and inference for a wide range of COVID-19 mitigation and suppression policy measures. Moreover, the algorithm is able to support efficient testing in a test-trace-isolate approach to contain COVID-19 infection spread. To the best of our knowledge, this is the first model with efficient inference for COVID-19 infection spread based on individual-level contact data; most epidemic models are macro-level models that reason over entire populations. The implementation of CRISP is available in Python and C++ at https://github.com/zalandoresearch/CRISP.

Historically, machine learning methods have not been designed with security in mind. In turn, this has given rise to adversarial examples, carefully perturbed input samples aimed to mislead detection at test time, which have been applied to attack spam and malware classification, and more recently to attack image classification. Consequently, an abundance of research has been devoted to designing machine learning methods that are robust to adversarial examples. Unfortunately, there are desiderata besides robustness that a secure and safe machine learning model must satisfy, such as fairness and privacy. Recent work by Song et al. (2019) has shown, empirically, that there exists a trade-off between robust and private machine learning models. Models designed to be robust to adversarial examples often overfit on training data to a larger extent than standard (non-robust) models. If a dataset contains private information, then any statistical test that separates training and test data by observing a model's outputs can represent a privacy breach, and if a model overfits on training data, these statistical tests become easier. In this work, we identify settings where standard models will provably overfit to a larger extent in comparison to robust models, and as empirically observed in previous works, settings where the opposite behavior occurs. Thus, it is not necessarily the case that privacy must be sacrificed to achieve robustness. The degree of overfitting naturally depends on the amount of data available for training. We go on to formally characterize how the training set size factors into the privacy risks exposed by training a robust model. Finally, we empirically show our findings hold on image classification benchmark datasets, such as CIFAR-10.

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes (GPs). While the majority of prior literature on learning of GP-SSM are focused on processing a given set of time series data, data may arrive and accumulate sequentially over time in most dynamical systems. Storing all such sequential data and updating the model over entire data incur large amount of computational resources in space and time. To overcome this difficulty, we propose a practical method, termed \textit{onlineGPSSM}, that incorporates stochastic variational inference (VI) and online VI with novel formulation. The proposed method mitigates the computational complexity without catastrophic forgetting and also support adaptation to changes in a system and/or a real environments. Furthermore, we present application of onlineGPSSM into the reinforcement learning (RL) of partially observable dynamical systems by integrating onlineGPSSM with Bayesian filtering and trajectory optimization algorithms. Numerical examples are presented to demonstrate applicability of the proposed method.

With the development of Internet of Things (IoT), IoT intelligence becomes emerging technology. "Curse of Dimensionality" is the barrier of data fusion in edge devices for the success of IoT intelligence. A Linguistic Attribute Hierarchy (LAH), embedded with Linguistic Decision Trees (LDTs), can represent a new attribute deep learning. In contrast to the conventional deep learning, an LAH could overcome the shortcoming of missing interpretation by providing transparent information propagation through the rules, produced by LDTs in the LAH. Similar to the conventional deep learning, the computing complexity of optimising LAHs blocks the applications of LAHs. In this paper, we propose a heuristic approach to constructing an LAH, embedded with LDTs for decision making or classification by utilising the distance correlations between attributes and between attributes and the goal variable. The set of attributes is divided to some attribute clusters, and then they are heuristically organised to form a linguistic attribute hierarchy. The proposed approach was validated with some benchmark decision making or classification problems from the UCI machine learning repository. The experimental results show that the proposed self-organisation algorithm can construct an effective and efficient linguistic attribute hierarchy. Such a self-organised linguistic attribute hierarchy embedded with LDTs can not only efficiently tackle "curse of dimensionality" in a single LDT for data fusion with massive attributes, but also achieve better or comparable performance on decision making or classification, compared to the single LDT for the problem to be solved. The self-organisation algorithm is much efficient than the Genetic Algorithm in Wrapper for the optimisation of LAHs. This makes it feasible to embed the self-organisation algorithm in edge devices for IoT intelligence.

We propose to address the task of causal structure learning from data in a supervised manner. Existing work on learning causal directions by supervised learning is restricted to learning pairwise relation, and not well suited for whole DAG discovery. We propose a novel approach of modeling the whole DAG structure discovery as a supervised learning. To fit the problem in hand, we propose to use permutation equivariant models that align well with the problem domain. We evaluate the proposed approach extensively on synthetic graphs of size 10,20,50,100 and real data, and show promising results compared with a variety of previous approaches.