We study the problem of deployment efficient reinforcement learning (RL) with linear function approximation under the \emph{reward-free} exploration setting. This is a well-motivated problem because deploying new policies is costly in real-life RL applications. Under the linear MDP setting with feature dimension $d$ and planning horizon $H$, we propose a new algorithm that collects at most $\widetilde{O}(\frac{d^2H^5}{\epsilon^2})$ trajectories within $H$ deployments to identify $\epsilon$-optimal policy for any (possibly data-dependent) choice of reward functions. To the best of our knowledge, our approach is the first to achieve optimal deployment complexity and optimal $d$ dependence in sample complexity at the same time, even if the reward is known ahead of time. Our novel techniques include an exploration-preserving policy discretization and a generalized G-optimal experiment design, which could be of independent interest. Lastly, we analyze the related problem of regret minimization in low-adaptive RL and provide information-theoretic lower bounds for switching cost and batch complexity.

In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the dynamics in various time series. To address this problem, we propose a novel model-based time series clustering method with mixtures of linear Gaussian state space models, which have high flexibility. The proposed method uses a new expectation-maximization algorithm for the mixture model to estimate the model parameters, and determines the number of clusters using the Bayesian information criterion. Experiments on a simulated dataset demonstrate the effectiveness of the method in clustering, parameter estimation, and model selection. The method is applied to real datasets commonly used to evaluate time series clustering methods. Results showed that the proposed method produces clustering results that are as accurate or more accurate than those obtained using previous methods.

Feature selection is an effective preprocessing technique to reduce data dimension. For feature selection, rough set theory provides many measures, among which mutual information is one of the most important attribute measures. However, mutual information based importance measures are computationally expensive and inaccurate, especially in hypersample instances, and it is undoubtedly a NP-hard problem in high-dimensional hyperhigh-dimensional data sets. Although many representative group intelligent algorithm feature selection strategies have been proposed so far to improve the accuracy, there is still a bottleneck when using these feature selection algorithms to process high-dimensional large-scale data sets, which consumes a lot of performance and is easy to select weakly correlated and redundant features. In this study, we propose an incremental mutual information based improved swarm intelligent optimization method (IMIICSO), which uses rough set theory to calculate the importance of feature selection based on mutual information. This method extracts decision table reduction knowledge to guide group algorithm global search. By exploring the computation of mutual information of supersamples, we can not only discard the useless features to speed up the internal and external computation, but also effectively reduce the cardinality of the optimal feature subset by using IMIICSO method, so that the cardinality is minimized by comparison. The accuracy of feature subsets selected by the improved cockroach swarm algorithm based on incremental mutual information is better or almost the same as that of the original swarm intelligent optimization algorithm. Experiments using 10 datasets derived from UCI, including large scale and high dimensional datasets, confirmed the efficiency and effectiveness of the proposed algorithm.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

Prediction of multi-dimensional labels plays an important role in machine learning problems. We found that the classical binary labels could not reflect the contents and their relationships in an instance. Hence, we propose a multi-label classification model based on interval type-2 fuzzy logic. In the proposed model, we use a deep neural network to predict the type-1 fuzzy membership of an instance and another one to predict the fuzzifiers of the membership to generate interval type-2 fuzzy memberships. We also propose a loss function to measure the similarities between binary labels in datasets and interval type-2 fuzzy memberships generated by our model. The experiments validate that our approach outperforms baselines on multi-label classification benchmarks.

Determining the most informative features for predicting the overall survival of patients diagnosed with high-grade gastroenteropancreatic neuroendocrine neoplasms is crucial to improve individual treatment plans for patients, as well as the biological understanding of the disease. Recently developed ensemble feature selectors like the Repeated Elastic Net Technique for Feature Selection (RENT) and the User-Guided Bayesian Framework for Feature Selection (UBayFS) allow the user to identify such features in datasets with low sample sizes. While RENT is purely data-driven, UBayFS is capable of integrating expert knowledge a priori in the feature selection process. In this work we compare both feature selectors on a dataset comprising of 63 patients and 134 features from multiple sources, including basic patient characteristics, baseline blood values, tumor histology, imaging, and treatment information. Our experiments involve data-driven and expert-driven setups, as well as combinations of both. We use findings from clinical literature as a source of expert knowledge. Our results demonstrate that both feature selectors allow accurate predictions, and that expert knowledge has a stabilizing effect on the feature set, while the impact on predictive performance is limited. The features WHO Performance Status, Albumin, Platelets, Ki-67, Tumor Morphology, Total MTV, Total TLG, and SUVmax are the most stable and predictive features in our study.

The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply both to measure-theoretic probability (with standard Borel spaces) and beyond probability theory, including to deterministic and possibilistic networks. It therefore provides a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed random variables as well as deterministic and possibilistic variables.

Neuroscientific studies aim to find an accurate and reliable brain Effective Connectome (EC). Although current EC discovery methods have contributed to our understanding of brain organization, their performances are severely constrained by the short sample size and poor temporal resolution of fMRI data, and high dimensionality of the brain connectome. By leveraging the DTI data as prior knowledge, we introduce two Bayesian causal discovery frameworks -- the Bayesian GOLEM (BGOLEM) and Bayesian FGES (BFGES) methods -- that offer significantly more accurate and reliable ECs and address the shortcomings of the existing causal discovery methods in discovering ECs based on only fMRI data. Through a series of simulation studies on synthetic and hybrid (DTI of the Human Connectome Project (HCP) subjects and synthetic fMRI) data, we demonstrate the effectiveness of the proposed methods in discovering EC. To numerically assess the improvement in the accuracy of ECs with our method on empirical data, we first introduce the Pseudo False Discovery Rate (PFDR) as a new computational accuracy metric for causal discovery in the brain. We show that our Bayesian methods achieve higher accuracy than traditional methods on HCP data. Additionally, we measure the reliability of discovered ECs using the Rogers-Tanimoto index for test-retest data and show that our Bayesian methods provide significantly more reproducible ECs than traditional methods. Overall, our study's numerical and graphical results highlight the potential for these frameworks to advance our understanding of brain function and organization significantly.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances circumvent this challenge of discreteness by embedding discrete tokens as continuous surrogates, they still fall short of satisfactory generation quality. To understand this, we first dive deep into the denoised training protocol of diffusion-based sequence generative models and determine their three severe problems, i.e., 1) failing to learn, 2) lack of scalability, and 3) neglecting source conditions. We argue that these problems can be boiled down to the pitfall of the not completely eliminated discreteness in the embedding space, and the scale of noises is decisive herein. In this paper, we introduce DINOISER to facilitate diffusion models for sequence generation by manipulating noises. We propose to adaptively determine the range of sampled noise scales for counter-discreteness training; and encourage the proposed diffused sequence learner to leverage source conditions with amplified noise scales during inference. Experiments show that DINOISER enables consistent improvement over the baselines of previous diffusion-based sequence generative models on several conditional sequence modeling benchmarks thanks to both effective training and inference strategies. Analyses further verify that DINOISER can make better use of source conditions to govern its generative process.