We propose a unified framework for adaptive routing in multitask, multimodal prediction settings where data heterogeneity and task interactions vary across samples. We introduce a routing-based architecture that dynamically selects modality processing pathways and task-sharing strategies on a per-sample basis. Our model defines multiple modality paths, including raw and fused representations of text and numeric features, and learns to route each input through the most informative modality-task expert combination. Task-specific predictions are produced by shared or independent heads depending on the routing decision, and the entire system is trained end-to-end. We evaluate the model on both synthetic data and real-world psychotherapy notes, predicting depression and anxiety outcomes. Our experiments show that our method consistently outperforms fixed multitask or single-task baselines, and that the learned routing policy provides interpretable insights into modality relevance and task structure. This addresses critical challenges in personalized healthcare by providing per-subject adaptive information processing that accounts for data and task correlation heterogeneity.

In many science and engineering problems, we observe high-dimensional data acquired sequentially. At each time instant, these data correspond to one of a predefined number of classes. The sequence of classes follows a certain pattern, with the transition probabilities of the classes being unknown. Our hypothesized generative model of the observed data involves two latent processes. The first is a root process representing the sequence of classes, while the second is a low-dimensional process generated as a Markovian process, depending on the current class and the previous value of the low-dimensional process. The observed high-dimensional process is generated from the low-dimensional state process. Our objective is to infer the posterior distributions of the classes as they evolve over time based on the observed data and the adopted model. To achieve this, we propose a method for estimating the latent processes. We demonstrate the effectiveness of our approach on synthesized data.

In this article, we propose novel Gaussian process-gated hierarchical mixtures of experts (GPHMEs). Unlike other mixtures of experts with gating models linear in the input, our model employs gating functions built with Gaussian processes (GPs). These processes are based on random features that are non-linear functions of the inputs. Furthermore, the experts in our model are also constructed with GPs. The optimization of the GPHMEs is performed by variational inference. The proposed GPHMEs have several advantages. They outperform tree-based HME benchmarks that partition the data in the input space, and they achieve good performance with reduced complexity. Another advantage is the interpretability they provide for deep GPs, and more generally, for deep Bayesian neural networks. Our GPHMEs demonstrate excellent performance for large-scale data sets, even with quite modest sizes.

In many machine learning problems, one has to work with data of different types, including continuous, discrete, and categorical data. Further, it is often the case that many of these data are missing from the database. This paper proposes a Gaussian process framework that efficiently captures the information from mixed numerical and categorical data that effectively incorporates missing variables. First, we propose a generative model for the mixed-type data. The generative model exploits Gaussian processes with kernels constructed from the latent vectors. We also propose a method for inference of the unknowns, and in its implementation, we rely on a sparse spectrum approximation of the Gaussian processes and variational inference. We demonstrate the performance of the method for both supervised and unsupervised tasks. First, we investigate the imputation of missing variables in an unsupervised setting, and then we show the results of joint imputation and classification on IBM employee data.

In science and engineering, we often deal with signals that are acquired from time-varying systems represented by dynamic graphs. We observe these signals, and the interest is in finding the time-varying topology of the graphs. We propose two Bayesian methods for estimating these topologies without assuming any specific functional relationships among the signals on the graphs. The two methods exploit Gaussian processes, where the first method uses the length scale of the kernel and relies on variational inference for optimization, and the second method is based on derivatives of the functions and Monte Carlo sampling. Both methods estimate the time-varying topologies of the graphs sequentially. We provide numerical tests that show the performance of the methods in two settings.

During the process of childbirth, fetal distress caused by hypoxia can lead to various abnormalities. Cardiotocography (CTG), which consists of continuous recording of the fetal heart rate (FHR) and uterine contractions (UC), is routinely used for classifying the fetuses as hypoxic or non-hypoxic. In practice, we face highly imbalanced data, where the hypoxic fetuses are significantly underrepresented. We propose to address this problem by boost ensemble learning, where for learning, we use the distribution of classification error over the dataset. We then iteratively select the most informative majority data samples according to this distribution. In our work, in addition to addressing the imbalanced problem, we also experimented with features that are not commonly used in obstetrics. We extracted a large number of statistical features of fetal heart tracings and uterine activity signals and used only the most informative ones. For classification, we implemented several methods: Random Forest, AdaBoost, k-Nearest Neighbors, Support Vector Machine, and Decision Trees. The paper provides a comparison in the performance of these methods on fetal heart rate tracings available from a public database. Our results on the publicly available Czech database show that most applied methods improved their performances considerably when boost ensemble was used.