Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-functions and view a deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a natural idea to combine DQN and an existing few-shot learning method, we identify that such a direct combination does not perform well due to severe overfitting, which is particularly critical in BO due to the need of a versatile sampling policy. To address this, we present a Bayesian variant of DQN with the following three features: (i) It learns a distribution of Q-networks as AFs based on the Kullback-Leibler regularization framework. This inherently provides the uncertainty required in sampling for BO and mitigates overfitting. (ii) For the prior of the Bayesian DQN, we propose to use a demo policy induced by an off-the-shelf AF for better training stability. (iii) On the meta-level, we leverage the meta-loss of Bayesian model-agnostic meta-learning, which serves as a natural companion to the proposed FSAF. Moreover, with the proper design of the Q-networks, FSAF is general-purpose in that it is agnostic to the dimension and the cardinality of the input domain. Through extensive experiments, we demonstrate that the FSAF achieves comparable or better regrets than the state-of-the-art benchmarks on a wide variety of synthetic and real-world test functions.

This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context, we show that the corresponding optimization problem can be reformulated as a non-negative penalized linear regression problem. This reformulation allows us to propose novel algorithms inspired from inverse problems and nonnegative matrix factorization. In particular, we consider majorization-minimization which leads in our setting to efficient multiplicative updates for a variety of penalties. Furthermore, we derive for the first time an efficient algorithm to compute the regularization path of UOT with quadratic penalties. The proposed algorithm provides a continuity of piece-wise linear OT plans converging to the solution of balanced OT (corresponding to infinite penalty weights). We perform several numerical experiments on simulated and real data illustrating the new algorithms, and provide a detailed discussion about more sophisticated optimization tools that can further be used to solve OT problems thanks to our reformulation.

In reality, learning from multi-view multi-label data inevitably confronts three challenges: missing labels, incomplete views, and non-aligned views. Existing methods mainly concern the first two and commonly need multiple assumptions to attack them, making even state-of-the-arts involve at least two explicit hyper-parameters such that model selection is quite difficult. More roughly, they will fail in handling the third challenge, let alone addressing the three jointly. In this paper, we aim at meeting these under the least assumption by building a concise yet effective model with just one hyper-parameter. To ease insufficiency of available labels, we exploit not only the consensus of multiple views but also the global and local structures hidden among multiple labels. Specifically, we introduce an indicator matrix to tackle the first two challenges in a regression form while aligning the same individual labels and all labels of different views in a common label space to battle the third challenge. In aligning, we characterize the global and local structures of multiple labels to be high-rank and low-rank, respectively. Subsequently, an efficient algorithm with linear time complexity in the number of samples is established. Finally, even without view-alignment, our method substantially outperforms state-of-the-arts with view-alignment on five real datasets.

Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.

We present an efficient stochastic algorithm (RSG+) for canonical correlation analysis (CCA) using a reparametrization of the projection matrices. We show how this reparametrization (into structured matrices), simple in hindsight, directly presents an opportunity to repurpose/adjust mature techniques for numerical optimization on Riemannian manifolds. Our developments nicely complement existing methods for this problem which either require $O(d^3)$ time complexity per iteration with $O(\frac{1}{\sqrt{t}})$ convergence rate (where $d$ is the dimensionality) or only extract the top $1$ component with $O(\frac{1}{t})$ convergence rate. In contrast, our algorithm offers a strict improvement for this classical problem: it achieves $O(d^2k)$ runtime complexity per iteration for extracting the top $k$ canonical components with $O(\frac{1}{t})$ convergence rate. While the paper primarily focuses on the formulation and technical analysis of its properties, our experiments show that the empirical behavior on common datasets is quite promising. We also explore a potential application in training fair models where the label of protected attribute is missing or otherwise unavailable.

Distilling analytical models from data has the potential to advance our understanding and prediction of nonlinear dynamics. Although discovery of governing equations based on observed system states (e.g., trajectory time series) has revealed success in a wide range of nonlinear dynamics, uncovering the closed-form equations directly from raw videos still remains an open challenge. To this end, we introduce a novel end-to-end unsupervised deep learning framework to uncover the mathematical structure of equations that governs the dynamics of moving objects in videos. Such an architecture consists of (1) an encoder-decoder network that learns low-dimensional spatial/pixel coordinates of the moving object, (2) a learnable Spatial-Physical Transformation component that creates mapping between the extracted spatial/pixel coordinates and the latent physical states of dynamics, and (3) a numerical integrator-based sparse regression module that uncovers the parsimonious closed-form governing equations of learned physical states and, meanwhile, serves as a constraint to the autoencoder. The efficacy of the proposed method is demonstrated by uncovering the governing equations of a variety of nonlinear dynamical systems depicted by moving objects in videos. The resulting computational framework enables discovery of parsimonious interpretable model in a flexible and accessible sensing environment where only videos are available.

The randomized or cross-validated split of training and testing sets has been adopted as the gold standard of machine learning for decades. The establishment of these split protocols are based on two assumptions: (i)-fixing the dataset to be eternally static so we could evaluate different machine learning algorithms or models; (ii)-there is a complete set of annotated data available to researchers or industrial practitioners. However, in this article, we intend to take a closer and critical look at the split protocol itself and point out its weakness and limitation, especially for industrial applications. In many real-world problems, we must acknowledge that there are numerous situations where assumption (ii) does not hold. For instance, for interdisciplinary applications like drug discovery, it often requires real lab experiments to annotate data which poses huge costs in both time and financial considerations. In other words, it can be very difficult or even impossible to satisfy assumption (ii). In this article, we intend to access this problem and reiterate the paradigm of active learning, and investigate its potential on solving problems under unconventional train/test split protocols. We further propose a new adaptive active learning architecture (AAL) which involves an adaptation policy, in comparison with the traditional active learning that only unidirectionally adds data points to the training pool. We primarily justify our points by extensively investigating an interdisciplinary drug-protein binding problem. We additionally evaluate AAL on more conventional machine learning benchmarking datasets like CIFAR-10 to demonstrate the generalizability and efficacy of the new framework.

Entity Matching (EM) aims at recognizing entity records that denote the same real-world object. Neural EM models learn vector representation of entity descriptions and match entities end-to-end. Though robust, these methods require many resources for training, and lack of interpretability. In this paper, we propose a novel EM framework that consists of Heterogeneous Information Fusion (HIF) and Key Attribute Tree (KAT) Induction to decouple feature representation from matching decision. Using self-supervised learning and mask mechanism in pre-trained language modeling, HIF learns the embeddings of noisy attribute values by inter-attribute attention with unlabeled data. Using a set of comparison features and a limited amount of annotated data, KAT Induction learns an efficient decision tree that can be interpreted by generating entity matching rules whose structure is advocated by domain experts. Experiments on 6 public datasets and 3 industrial datasets show that our method is highly efficient and outperforms SOTA EM models in most cases. Our codes and datasets can be obtained from https://github.com/THU-KEG/HIF-KAT.

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most ``informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most ``informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in closed form, as these quantities require the evaluation of seldom tractable integrals. In this work, we present the marginalizable density model approximator (MDMA), a novel deep network architecture which provides closed form expressions for the probabilities, marginals and conditionals of any subset of the variables. The MDMA learns deep scalar representations for each individual variable and combines them via learned hierarchical tensor decompositions into a tractable yet expressive CDF, from which marginals and conditional densities are easily obtained. We illustrate the advantage of exact marginalizability in several tasks that are out of reach of previous deep network-based density estimation models, such as estimating mutual information between arbitrary subsets of variables, inferring causality by testing for conditional independence, and inference with missing data without the need for data imputation, outperforming state-of-the-art models on these tasks. The model also allows for parallelized sampling with only a logarithmic dependence of the time complexity on the number of variables.