This paper proposes a new classification model called logistic circuits. On MNIST and Fashion datasets, our learning algorithm outperforms neural networks that have an order of magnitude more parameters. Yet, logistic circuits have a distinct origin in symbolic AI, forming a discriminative counterpart to probabilistic-logical circuits such as ACs, SPNs, and PSDDs. We show that parameter learning for logistic circuits is convex optimization, and that a simple local search algorithm can induce strong model structures from data.

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable variational inference procedures based on the idea of particle optimization have been proposed. These methods directly optimize a set of particles to approximate the target posterior. However, their application to BNNs often yields sub-optimal performance, as such methods have a particular failure mode on over-parameterized models. In this paper, we propose to solve this issue by performing particle optimization directly in the space of regression functions. We demonstrate through extensive experiments that our method successfully overcomes this issue, and outperforms strong baselines in a variety of tasks including prediction, defense against adversarial examples, and reinforcement learning.

The subject of this article is the introduction of a weaker concept of well-posedness of Bayesian inverse problems. The conventional concept of (`Lipschitz') well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice, especially when considering blackbox models, and probably too strong in many contexts. Our concept replaces the Lipschitz continuity of the posterior measure in the Hellinger distance by just continuity. This weakening is tolerable, since the continuity is in general only used as a stability criterion. The main result of this article is a proof of well-posedness for a large class of Bayesian inverse problems, where very little or no information about the underlying model is available. It includes any Bayesian inverse problem arising when observing finite-dimensional data perturbed by additive, non-degenerate Gaussian noise. Moreover, well-posedness with respect to other probability metrics is investigated, including weak convergence, total variation, Wasserstein, and also the Kullback-Leibler divergence.

Currently, college-going students are taking longer to graduate than their parental generations. Further, in the United States, the six-year graduation rate has been 59% for decades. Improving the educational quality by training better-prepared students who can successfully graduate in a timely manner is critical. Accurately predicting students' grades in future courses has attracted much attention as it can help identify at-risk students early so that personalized feedback can be provided to them on time by advisors. Prior research on students' grade prediction include shallow linear models; however, students' learning is a highly complex process that involves the accumulation of knowledge across a sequence of courses that can not be sufficiently modeled by these linear models. In addition to that, prior approaches focus on prediction accuracy without considering prediction uncertainty, which is essential for advising and decision making. In this work, we present two types of Bayesian deep learning models for grade prediction. The MLP ignores the temporal dynamics of students' knowledge evolution. Hence, we propose RNN for students' performance prediction. To evaluate the performance of the proposed models, we performed extensive experiments on data collected from a large public university. The experimental results show that the proposed models achieve better performance than prior state-of-the-art approaches. Besides more accurate results, Bayesian deep learning models estimate uncertainty associated with the predictions. We explore how uncertainty estimation can be applied towards developing a reliable educational early warning system. In addition to uncertainty, we also develop an approach to explain the prediction results, which is useful for advisors to provide personalized feedback to students.

Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We show how the missing-value problem fits neatly into the overall framework of optimal clustering by incorporating the missing value mechanism into the random labeled point process and then marginalizing out the missing-value process. In particular, we demonstrate the proposed framework for the Gaussian model with arbitrary covariance structures. Comprehensive experimental studies on both synthetic and real-world RNA-seq data show the superior performance of the proposed optimal clustering with missing values when compared to various clustering approaches. Optimal clustering with missing values obviates the need for imputation-based pre-processing of the data, while at the same time possessing smaller clustering errors.

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and cannot handle complex structured data. In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}. More specifically, in order to apply Bayesian optimization to structured data, we extract useful topological information from a structure and measure the proper similarity between structures. To this end, we utilize persistent homology, which is a topological data analysis method that was recently applied in machine learning. Moreover, we propose the Bayesian optimization algorithm that can handle multiple types of topological information by using a linear combination of kernels for persistence diagrams. Through experiments, we show that topological information extracted by persistent homology contributes to a more efficient search for optimal structures compared to the random search baseline and the graph Bayesian optimization algorithm.

Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning algorithm to utilize the structural information and further make use of unlabeled and weakly-labeled data. We use a generative model to leverage the large amount of unlabeled data and introduce path constraints into the learning algorithm to incorporate the structural information of the class hierarchy. The posterior probabilities of both unlabeled and weakly labeled data can be incorporated with path-dependent scores. Since we put a structure-sensitive cost to the learning algorithm to constrain the classification consistent with the class hierarchy and do not need to reconstruct the feature vectors for different structures, we can significantly reduce the computational cost compared to structural output learning. Experimental results on two hierarchical text classification benchmarks show that our approach is not only effective but also efficient to handle the semi-supervised and weakly supervised hierarchical text classification.

Recent advances in conditional image generation tasks, such as image-to-image translation and image inpainting, are largely accounted to the success of conditional GAN models, which are often optimized by the joint use of the GAN loss with the reconstruction loss However, we reveal that this training recipe shared by almost all existing methods causes one critical side effect: lack of diversity in output samples. In order to accomplish both training stability and multimodal output generation, we propose novel training schemes with a new set of losses named moment reconstruction losses that simply replace the reconstruction loss. We show that our approach is applicable to any conditional generation tasks by performing thorough experiments on image-to-image translation, super-resolution and image inpainting using Cityscapes and CelebA dataset. Quantitative evaluations also confirm that our methods achieve a great diversity in outputs while retaining or even improving the visual fidelity of generated samples. Recently, active research has led to a huge progress on conditional image generation, whose typical tasks include image-to-image translation (Isola et al. (2017)), image inpainting (Pathak et al. (2016)), super-resolution (Ledig et al. (2017)) and video prediction (Mathieu et al. (2016)). At the core of such advances is the success of conditional GANs (Mirza & Osindero (2014)), which improve GANs by allowing the generator to take an additional code or condition to control the modes of the data being generated. However, training GANs, including conditional GANs, is highly unstable and easy to collapse (Goodfellow et al. (2014)). Indeed, using these two types of losses is synergetic in that the GAN loss complements the weakness of the reconstruction loss that output samples are blurry and lack high-frequency structure, while the reconstruction loss offers the training stability required for convergence. In spite of its success, we argue that it causes one critical side effect; the reconstruction loss aggravates the mode collapse, one of notorious problems of GANs. In conditional generation tasks, which are to intrinsically learn one-to-many mappings, the model is expected to generate diverse outputs from a single conditional input, depending on some stochastic variables (e.g.

With the increasing variety of services that e-commerce platforms provide, criteria for evaluating their success become also increasingly multi-targeting. This work introduces a multi-target optimization framework with Bayesian modeling of the target events, called Deep Bayesian Multi-Target Learning (DBMTL). In this framework, target events are modeled as forming a Bayesian network, in which directed links are parameterized by hidden layers, and learned from training samples. The structure of Bayesian network is determined by model selection. We applied the framework to Taobao live-streaming recommendation, to simultaneously optimize (and strike a balance) on targets including click-through rate, user stay time in live room, purchasing behaviors and interactions. Significant improvement has been observed for the proposed method over other MTL frameworks and the non-MTL model. Our practice shows that with an integrated causality structure, we can effectively make the learning of a target benefit from other targets, creating significant synergy effects that improve all targets. The neural network construction guided by DBMTL fits in with the general probabilistic model connecting features and multiple targets, taking weaker assumption than the other methods discussed in this paper. This theoretical generality brings about practical generalization power over various targets distributions, including sparse targets and continuous-value ones.

Traditional models of rational action treat the agent as though it is cleanly separated from its environment, and can act on that environment from the outside. Such agents have a known functional relationship with their environment, can model their environment in every detail, and do not need to reason about themselves or their internal parts. We provide an informal survey of obstacles to formalizing good reasoning for agents embedded in their environment. Such agents must optimize an environment that is not of type ``function''; they must rely on models that fit within the modeled environment; and they must reason about themselves as just another physical system, made of parts that can be modified and that can work at cross purposes.