Boosting is a commonly used technique to enhance the performance of a set of base models by combining them into a strong ensemble model. Though widely adopted, boosting is typically used in supervised learning where the data is labeled accurately. However, in weakly supervised learning, where most of the data is labeled through weak and noisy sources, it remains nontrivial to design effective boosting approaches. In this work, we show that the standard implementation of the convex combination of base learners can hardly work due to the presence of noisy labels. Instead, we propose $\textit{LocalBoost}$, a novel framework for weakly-supervised boosting. LocalBoost iteratively boosts the ensemble model from two dimensions, i.e., intra-source and inter-source. The intra-source boosting introduces locality to the base learners and enables each base learner to focus on a particular feature regime by training new base learners on granularity-varying error regions. For the inter-source boosting, we leverage a conditional function to indicate the weak source where the sample is more likely to appear. To account for the weak labels, we further design an estimate-then-modify approach to compute the model weights. Experiments on seven datasets show that our method significantly outperforms vanilla boosting methods and other weakly-supervised methods.

This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs (MM-DAGs), which are commonly observed in complex systems, e.g., traffic, manufacturing, and weather systems, whose variables are multi-modal with scalars, vectors, and functions. This paper takes the traffic congestion analysis as a concrete case, where a traffic intersection is usually regarded as a DAG. In a road network of multiple intersections, different intersections can only have some overlapping and distinct variables observed. For example, a signalized intersection has traffic light-related variables, whereas unsignalized ones do not. This encourages the multi-task design: with each DAG as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their consensus and consistency are maximized. To this end, we innovatively propose a multi-modal regression for linear causal relationship description of different variables. Then we develop a novel Causality Difference (CD) measure and its differentiable approximator. Compared with existing SOTA measures, CD can penalize the causal structural difference among DAGs with distinct nodes and can better consider the uncertainty of causal orders. We rigidly prove our design's topological interpretation and consistency properties. We conduct thorough simulations and one case study to show the effectiveness of our MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG

We argue that for analysis of Positive Unlabeled (PU) data under Selected Completely At Random (SCAR) assumption it is fruitful to view the problem as fitting of misspecified model to the data. Namely, we show that the results on misspecified fit imply that in the case when posterior probability of the response is modelled by logistic regression, fitting the logistic regression to the observable PU data which {\it does not} follow this model, still yields the vector of estimated parameters approximately colinear with the true vector of parameters. This observation together with choosing the intercept of the classifier based on optimisation of analogue of F1 measure yields a classifier which performs on par or better than its competitors on several real data sets considered.

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an efficient Gibbs sampler. The Gibbs sampler attains similar performances as the state-of-the-art Monte Carlo Markov chain methods, such as the Hamiltonian Monte Carlo or the Metropolis adjusted Langevin algorithm, both on real and synthetic data. By framing our analysis in the teacher-student setting, we introduce a thermalization criterion that allows us to detect when an algorithm, when run on data with synthetic labels, fails to sample from the posterior. The criterion is based on the fact that in the teacher-student setting we can initialize an algorithm directly at equilibrium.

Neural QCFG is a grammar-based sequence-tosequence (seq2seq) model with strong inductive biases on hierarchical structures. It excels in interpretability and generalization but suffers from expensive inference. In this paper, we study two low-rank variants of Neural QCFG for faster inference with different trade-offs between efficiency and expressiveness. Furthermore, utilizing the symbolic interface provided by the grammar, we introduce two soft constraints over tree hierarchy and source coverage. We experiment with various datasets and find that our models outperform vanilla Neural QCFG in most settings.

In this paper, we study the problem of (finite horizon tabular) Markov decision processes (MDPs) with heavy-tailed rewards under the constraint of differential privacy (DP). Compared with the previous studies for private reinforcement learning that typically assume rewards are sampled from some bounded or sub-Gaussian distributions to ensure DP, we consider the setting where reward distributions have only finite $(1+v)$-th moments with some $v \in (0,1]$. By resorting to robust mean estimators for rewards, we first propose two frameworks for heavy-tailed MDPs, i.e., one is for value iteration and another is for policy optimization. Under each framework, we consider both joint differential privacy (JDP) and local differential privacy (LDP) models. Based on our frameworks, we provide regret upper bounds for both JDP and LDP cases and show that the moment of distribution and privacy budget both have significant impacts on regrets. Finally, we establish a lower bound of regret minimization for heavy-tailed MDPs in JDP model by reducing it to the instance-independent lower bound of heavy-tailed multi-armed bandits in DP model. We also show the lower bound for the problem in LDP by adopting some private minimax methods. Our results reveal that there are fundamental differences between the problem of private RL with sub-Gaussian and that with heavy-tailed rewards.

Measuring the intensity of events is crucial for monitoring and tracking armed conflict. Advances in automated event extraction have yielded massive data sets of "who did what to whom" micro-records that enable data-driven approaches to monitoring conflict. The Goldstein scale is a widely-used expert-based measure that scores events on a conflictual-cooperative scale. It is based only on the action category ("what") and disregards the subject ("who") and object ("to whom") of an event, as well as contextual information, like associated casualty count, that should contribute to the perception of an event's "intensity". This paper takes a latent variable-based approach to measuring conflict intensity. We introduce a probabilistic generative model that assumes each observed event is associated with a latent intensity class. A novel aspect of this model is that it imposes an ordering on the classes, such that higher-valued classes denote higher levels of intensity. The ordinal nature of the latent variable is induced from naturally ordered aspects of the data (e.g., casualty counts) where higher values naturally indicate higher intensity. We evaluate the proposed model both intrinsically and extrinsically, showing that it obtains comparatively good held-out predictive performance.

Adverse posttraumatic neuropsychiatric sequelae (APNS) are common among veterans and millions of Americans after traumatic exposures, resulting in substantial burdens for trauma survivors and society. Despite numerous studies conducted on APNS over the past decades, there has been limited progress in understanding the underlying neurobiological mechanisms due to several unique challenges. One of these challenges is the reliance on subjective self-report measures to assess APNS, which can easily result in measurement errors and biases (e.g., recall bias). To mitigate this issue, in this paper, we investigate the potential of leveraging the objective longitudinal mobile device data to identify homogeneous APNS states and study the dynamic transitions and potential risk factors of APNS after trauma exposure. To handle specific challenges posed by longitudinal mobile device data, we developed exploratory hidden Markov factor models and designed a Stabilized Expectation-Maximization algorithm for parameter estimation. Simulation studies were conducted to evaluate the performance of parameter estimation and model selection. Finally, to demonstrate the practical utility of the method, we applied it to mobile device data collected from the Advancing Understanding of RecOvery afteR traumA (AURORA) study.

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), and a recently proposed hybrid method called KalmanNet.

Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies mainly focus on finite state settings, and do not directly apply to these models. To overcome this lacuna, in this work we study the problem of optimal control of a family of discrete-time countable state-space Markov Decision Processes (MDPs) governed by an unknown parameter $\theta\in\Theta$, and defined on a countably-infinite state space $\mathcal X=\mathbb{Z}_+^d$, with finite action space $\mathcal A$, and an unbounded cost function. We take a Bayesian perspective with the random unknown parameter $\boldsymbol{\theta}^*$ generated via a given fixed prior distribution on $\Theta$. To optimally control the unknown MDP, we propose an algorithm based on Thompson sampling with dynamically-sized episodes: at the beginning of each episode, the posterior distribution formed via Bayes' rule is used to produce a parameter estimate, which then decides the policy applied during the episode. To ensure the stability of the Markov chain obtained by following the policy chosen for each parameter, we impose ergodicity assumptions. From this condition and using the solution of the average cost Bellman equation, we establish an $\tilde O(\sqrt{|\mathcal A|T})$ upper bound on the Bayesian regret of our algorithm, where $T$ is the time-horizon. Finally, to elucidate the applicability of our algorithm, we consider two different queuing models with unknown dynamics, and show that our algorithm can be applied to develop approximately optimal control algorithms.