Selecting an effective training signal for tasks in natural language processing is difficult: expert annotations are expensive, and crowd-sourced annotations may not be reliable. At the same time, recent work in NLP has demonstrated that learning from a distribution over labels acquired from crowd annotations can be effective. However, there are many ways to acquire such a distribution, and the performance allotted by any one method can fluctuate based on the task and the amount of available crowd annotations, making it difficult to know a priori which distribution is best. This paper systematically analyzes this in the out-of-domain setting, adding to the NLP literature which has focused on in-domain evaluation, and proposes new methods for acquiring soft-labels from crowd-annotations by aggregating the distributions produced by existing methods. In particular, we propose to aggregate multiple-views of crowd annotations via temperature scaling and finding their Jensen-Shannon centroid. We demonstrate that these aggregation methods lead to the most consistent performance across four NLP tasks on out-of-domain test sets, mitigating fluctuations in performance from the individual distributions. Additionally, aggregation results in the most consistently well-calibrated uncertainty estimation. We argue that aggregating different views of crowd-annotations is an effective and minimal intervention to acquire soft-labels which induce robust classifiers despite the inconsistency of the individual soft-labeling methods.

Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Clinically relevant and interpretable results require a framework that can (i) infer temporal interactions across multiple patient features found in EMR data (e.g., Labs, vital signs, etc.) and (ii) identify patterns that precede and are specific to an impending adverse event (e.g., sepsis). In this work, we propose a linear multivariate Hawkes process model, coupled with ReLU link function, to recover a Granger Causal (GC) graph with both exciting and inhibiting effects. We develop a scalable two-phase gradient-based method to obtain a maximum surrogate-likelihood estimator, which is shown to be effective via extensive numerical simulation. Our method is subsequently extended to a data set of patients admitted to Grady hospital system in Atlanta, GA, USA, where the estimated GC graph identifies several highly interpretable GC chains that precede sepsis. The code is available at \url{https://github.com/SongWei-GT/two-phase-MHP}.

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks. Several methods, ranging from temperature scaling to different Bayesian treatments of neural networks, have been proposed to mitigate overconfidence, most often supported by the numerical observation that they yield better calibrated uncertainty measures. In this work, we provide a sharp comparison between popular uncertainty measures for binary classification in a mathematically tractable model for overparametrized neural networks: the random features model. We discuss a trade-off between classification accuracy and calibration, unveiling a double descent like behavior in the calibration curve of optimally regularized estimators as a function of overparametrization. This is in contrast with the empirical Bayes method, which we show to be well calibrated in our setting despite the higher generalization error and overparametrization.

Existing models in cognitive science typically assume human categorization as graded generalization behavior in a multidimensional psychological space. However, category representations in these models may suffer from the curse of dimensionality in a natural setting. People generally rely on a tractable yet sufficient set of features to understand the complex environment. We propose a rational model of categorization based on a hierarchical mixture of probabilistic principal components, that simultaneously learn category representations and an economical collection of features. The model captures dimensional biases in human categorization and supports zero-shot learning. We further exploit a generative process within a low-dimensional latent space to provide a better account of categorization with high-dimensional stimuli.

Probabilistic logical rule learning has shown great strength in logical rule mining and knowledge graph completion. It learns logical rules to predict missing edges by reasoning on existing edges in the knowledge graph. However, previous efforts have largely been limited to only modeling chain-like Horn clauses such as $R_1(x,z)\land R_2(z,y)\Rightarrow H(x,y)$. This formulation overlooks additional contextual information from neighboring sub-graphs of entity variables $x$, $y$ and $z$. Intuitively, there is a large gap here, as local sub-graphs have been found to provide important information for knowledge graph completion. Inspired by these observations, we propose Logical Entity RePresentation (LERP) to encode contextual information of entities in the knowledge graph. A LERP is designed as a vector of probabilistic logical functions on the entity's neighboring sub-graph. It is an interpretable representation while allowing for differentiable optimization. We can then incorporate LERP into probabilistic logical rule learning to learn more expressive rules. Empirical results demonstrate that with LERP, our model outperforms other rule learning methods in knowledge graph completion and is comparable or even superior to state-of-the-art black-box methods. Moreover, we find that our model can discover a more expressive family of logical rules. LERP can also be further combined with embedding learning methods like TransE to make it more interpretable.

Probabilistic graphical models have become an important unsupervised learning tool for detecting network structures for a variety of problems, including the estimation of functional neuronal connectivity from two-photon calcium imaging data. However, in the context of calcium imaging, technological limitations only allow for partially overlapping layers of neurons in a brain region of interest to be jointly recorded. In this case, graph estimation for the full data requires inference for edge selection when many pairs of neurons have no simultaneous observations. This leads to the Graph Quilting problem, which seeks to estimate a graph in the presence of block-missingness in the empirical covariance matrix. Solutions for the Graph Quilting problem have previously been studied for Gaussian graphical models; however, neural activity data from calcium imaging are often non-Gaussian, thereby requiring a more flexible modeling approach. Thus, in our work, we study two approaches for nonparanormal Graph Quilting based on the Gaussian copula graphical model, namely a maximum likelihood procedure and a low-rank based framework. We provide theoretical guarantees on edge recovery for the former approach under similar conditions to those previously developed for the Gaussian setting, and we investigate the empirical performance of both methods using simulations as well as real data calcium imaging data. Our approaches yield more scientifically meaningful functional connectivity estimates compared to existing Gaussian graph quilting methods for this calcium imaging data set.

Multilayer networks are in the focus of the current complex network study. In such networks multiple types of links may exist as well as many attributes for nodes. To fully use multilayer -- and other types of complex networks in applications, the merging of various data with topological information renders a powerful analysis. First, we suggest a simple way of representing network data in a data matrix where rows correspond to the nodes, and columns correspond to the data items. The number of columns is allowed to be arbitrary, so that the data matrix can be easily expanded by adding columns. The data matrix can be chosen according to targets of the analysis, and may vary a lot from case to case. Next, we partition the rows of the data matrix into communities using a method which allows maximal compression of the data matrix. For compressing a data matrix, we suggest to extend so called regular decomposition method for non-square matrices. We illustrate our method for several types of data matrices, in particular, distance matrices, and matrices obtained by augmenting a distance matrix by a column of node degrees, or by concatenating several distances matrices corresponding to layers of a multilayer network. We illustrate our method with synthetic power-law graphs and two real networks: an Internet autonomous systems graph and a world airline graph. We compare the outputs of different community recovery methods on these graphs, and discuss how incorporating node degrees as a separate column to the data matrix leads our method to identify community structures well-aligned with tiered hierarchical structures commonly encountered in complex scale-free networks.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Federated Learning (FL) is a distributed learning scheme to train a shared model across clients. One common and fundamental challenge in FL is that the sets of data across clients could be non-identically distributed and have different sizes. Personalized Federated Learning (PFL) attempts to solve this challenge via locally adapted models. In this work, we present a novel framework for PFL based on hierarchical Bayesian modeling and variational inference. A global model is introduced as a latent variable to augment the joint distribution of clients' parameters and capture the common trends of different clients, optimization is derived based on the principle of maximizing the marginal likelihood and conducted using variational expectation maximization. Our algorithm gives rise to a closed-form estimation of a confidence value which comprises the uncertainty of clients' parameters and local model deviations from the global model. The confidence value is used to weigh clients' parameters in the aggregation stage and adjust the regularization effect of the global model. We evaluate our method through extensive empirical studies on multiple datasets. Experimental results show that our approach obtains competitive results under mild heterogeneous circumstances while significantly outperforming state-of-the-art PFL frameworks in highly heterogeneous settings. Our code is available at https://github.com/JunyiZhu-AI/confidence_aware_PFL.

Standard model-based reinforcement learning (MBRL) approaches fit a transition model of the environment to all past experience, but this wastes model capacity on data that is irrelevant for policy improvement. We instead propose a new "transition occupancy matching" (TOM) objective for MBRL model learning: a model is good to the extent that the current policy experiences the same distribution of transitions inside the model as in the real environment. We derive TOM directly from a novel lower bound on the standard reinforcement learning objective. To optimize TOM, we show how to reduce it to a form of importance weighted maximum-likelihood estimation, where the automatically computed importance weights identify policy-relevant past experiences from a replay buffer, enabling stable optimization. TOM thus offers a plug-and-play model learning sub-routine that is compatible with any backbone MBRL algorithm. On various Mujoco continuous robotic control tasks, we show that TOM successfully focuses model learning on policy-relevant experience and drives policies faster to higher task rewards than alternative model learning approaches. Code can be found on our project website: penn-pal-lab.github.io/TOM/