We develop a Bayesian semi-parametric model for the estimating the impact of dynamic treatment rules on survival among patients diagnosed with pediatric acute myeloid leukemia (AML). The data consist of a subset of patients enrolled in the phase III AAML1031 clinical trial in which patients move through a sequence of four treatment courses. At each course, they undergo treatment that may or may not include anthracyclines (ACT). While ACT is known to be effective at treating AML, it is also cardiotoxic and can lead to early death for some patients. Our task is to estimate the potential survival probability under hypothetical dynamic ACT treatment strategies, but there are several impediments. First, since ACT was not randomized in the trial, its effect on survival is confounded over time. Second, subjects initiate the next course depending on when they recover from the previous course, making timing potentially informative of subsequent treatment and survival. Third, patients may die or drop out before ever completing the full treatment sequence. We develop a generative Bayesian semi-parametric model based on Gamma Process priors to address these complexities. At each treatment course, the model captures subjects' transition to subsequent treatment or death in continuous time under a given rule. A g-computation procedure is used to compute a posterior over potential survival probability that is adjusted for time-varying confounding. Using this approach, we conduct posterior inference for the efficacy of hypothetical treatment rules that dynamically modify ACT based on evolving cardiac function.

A reliable pose estimator robust to environmental disturbances is desirable for mobile robots. To this end, inertial measurement units (IMUs) play an important role because they can perceive the full motion state of the vehicle independently. However, it suffers from accumulative error due to inherent noise and bias instability, especially for low-cost sensors. In our previous studies on Wheel-INS \cite{niu2021, wu2021}, we proposed to limit the error drift of the pure inertial navigation system (INS) by mounting an IMU to the wheel of the robot to take advantage of rotation modulation. However, Wheel-INS still drifted over a long period of time due to the lack of external correction signals. In this letter, we propose to exploit the environmental perception ability of Wheel-INS to achieve simultaneous localization and mapping (SLAM) with only one IMU. To be specific, we use the road bank angles (mirrored by the robot roll angles estimated by Wheel-INS) as terrain features to enable the loop closure with a Rao-Blackwellized particle filter. The road bank angle is sampled and stored according to the robot position in the grid maps maintained by the particles. The weights of the particles are updated according to the difference between the currently estimated roll sequence and the terrain map. Field experiments suggest the feasibility of the idea to perform SLAM in Wheel-INS using the robot roll angle estimates. In addition, the positioning accuracy is improved significantly (more than 30\%) over Wheel-INS. The source code of our implementation is publicly available (https://github.com/i2Nav-WHU/Wheel-SLAM).

We propose an analysis in fair learning that preserves the utility of the data while reducing prediction disparities under the criteria of group sufficiency. We focus on the scenario where the data contains multiple or even many subgroups, each with limited number of samples. As a result, we present a principled method for learning a fair predictor for all subgroups via formulating it as a bilevel objective. Specifically, the subgroup specific predictors are learned in the lower-level through a small amount of data and the fair predictor. In the upper-level, the fair predictor is updated to be close to all subgroup specific predictors. We further prove that such a bilevel objective can effectively control the group sufficiency and generalization error. We evaluate the proposed framework on real-world datasets. Empirical evidence suggests the consistently improved fair predictions, as well as the comparable accuracy to the baselines.

Binaural audio plays a significant role in constructing immersive augmented and virtual realities. As it is expensive to record binaural audio from the real world, synthesizing them from mono audio has attracted increasing attention. This synthesis process involves not only the basic physical warping of the mono audio, but also room reverberations and head/ear related filtrations, which, however, are difficult to accurately simulate in traditional digital signal processing. In this paper, we formulate the synthesis process from a different perspective by decomposing the binaural audio into a common part that shared by the left and right channels as well as a specific part that differs in each channel. Accordingly, we propose BinauralGrad, a novel two-stage framework equipped with diffusion models to synthesize them respectively. Specifically, in the first stage, the common information of the binaural audio is generated with a single-channel diffusion model conditioned on the mono audio, based on which the binaural audio is generated by a two-channel diffusion model in the second stage. Combining this novel perspective of two-stage synthesis with advanced generative models (i.e., the diffusion models), the proposed BinauralGrad is able to generate accurate and high-fidelity binaural audio samples. Experiment results show that on a benchmark dataset, BinauralGrad outperforms the existing baselines by a large margin in terms of both object and subject evaluation metrics (Wave L2: 0.128 vs. 0.157, MOS: 3.80 vs. 3.61).

The behaviour of statistical relational representations across differently sized domains has become a focal area of research from both a modelling and a complexity viewpoint.Recently, projectivity of a family of distributions emerged as a key property, ensuring that marginal probabilities are independent of the domain size. However, the formalisation used currently assumes that the domain is characterised only by its size. This contribution extends the notion of projectivity from families of distributions indexed by domain size to functors taking extensional data from a database. This makes projectivity available for the large range of applications taking structured input. We transfer key known results on projective families of distributions to the new setting. This includes a characterisation of projective fragments in different statistical relational formalisms as well as a general representation theorem for projective families of distributions. Furthermore, we prove a correspondence between projectivity and distributions on countably infinite domains, which we use to unify and generalise earlier work on statistical relational representations in infinite domains. Finally, we use the extended notion of projectivity to define a further strengthening, which we call $\sigma$-projectivity, and which allows the use of the same representation in different modes while retaining projectivity.

Predictive monitoring is a subfield of process mining that aims to predict how a running case will unfold in the future. One of its main challenges is forecasting the sequence of activities that will occur from a given point in time -- suffix prediction -- . Most approaches to the suffix prediction problem learn to predict the suffix by learning how to predict the next activity only, not learning from the whole suffix during the training phase. This paper proposes a novel architecture based on an encoder-decoder model with an attention mechanism that decouples the representation learning of the prefixes from the inference phase, predicting only the activities of the suffix. During the inference phase, this architecture is extended with a heuristic search algorithm that improves the selection of the activity for each index of the suffix. Our approach has been tested using 12 public event logs against 6 different state-of-the-art proposals, showing that it significantly outperforms these proposals.

Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a generative capacity to predict longitudinal time series data in these evolving graphs. However, parameter estimation within this framework fails to capture many real-world properties of social networks, including: triadic relationships, small world characteristics, and social learning theories which could be used to constrain the probabilistic estimation of dyadic covariates. Here, we propose triadic temporal exponential random graph models (TTERGM) to fill this void, which includes these hierarchical network relationships within the graph model. We represent social network learning theory as an additional probability distribution that optimizes Markov chains in the graph vector space. The new parameters are then approximated via Monte Carlo maximum likelihood estimation. We show that our TTERGM model achieves improved fidelity and more accurate predictions compared to several benchmark methods on GitHub network data.

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.

Bayesian adaptive experimental design is a form of active learning, which chooses samples to maximize the information they give about uncertain parameters. Prior work has shown that other forms of active learning can suffer from active learning bias, where unrepresentative sampling leads to inconsistent parameter estimates. We show that active learning bias can also afflict Bayesian adaptive experimental design, depending on model misspecification. We analyze the case of estimating a linear model, and show that worse misspecification implies more severe active learning bias. At the same time, model classes incorporating more "noise" -- i.e., specifying higher inherent variance in observations -- suffer less from active learning bias. Finally, we demonstrate empirically that insights from the linear model can predict the presence and degree of active learning bias in nonlinear contexts, namely in a (simulated) preference learning experiment. Statistical theory often assumes learners' access to large amounts of representative training data, drawn from the distribution which is the target of inference or prediction. Nonetheless, such access is not feasible for many applications. Training data may be scarce (e.g., learning to identify a rare medical condition; Henry, Hager, Pronovost, and Saria (2015)), difficult or expensive to obtain (e.g., requiring human coders for text; Chen, Lasko, Mei, Denny, and Xu (2015)), or time-consuming to collect (e.g., obtaining user preferences online; Cavagnaro, Gonzalez, Myung, and Pitt (2013); Golovin, Krause, and Ray (2010)). One response is to abandon random sampling for adaptive sampling methods, choosing data points in sequence to be as informative as possible.

This report summarises the outcomes of a systematic literature search to identify Bayesian network models used to support decision making in healthcare. After describing the search methodology, the selected research papers are briefly reviewed, with the view to identify publicly available models and datasets that are well suited to analysis using the causal interventional analysis software tool developed in Wang B, Lyle C, Kwiatkowska M (2021). Finally, an experimental evaluation of applying the software on a selection of models is carried out and preliminary results are reported.