AISTATS 2022 论文列表

A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are all Poisson processes. We develop an efficient posterior sampling via Markov chain Monte Carlo and use it for likelihood-based inference. Our method opens up room for the inference in sophisticated hierarchical point processes. We show in the experiments that more hidden Poisson processes brings better performance for likelihood fitting and events types prediction. We also compare our method with state-of-the-art models for temporal real-world datasets and demonstrate competitive abilities for both data fitting and prediction, using far fewer parameters.

Many applications, such as in physical simulation and engineering design, demand we estimate functions with high-dimensional outputs. To reduce the expensive cost of generating training examples, we usually choose several fidelities to enable a cost/quality trade-off. In this paper, we consider the active learning task to automatically identify the fidelities and training inputs to query new examples so as to achieve the best learning benefit-cost ratio. To this end, we propose DMFAL, a Deep Multi-Fidelity Active Learning approach. We first develop a deep neural network-based multi-fidelity model for high-dimensional outputs, which can flexibly capture strong complex correlations across the outputs and fidelities to enhance the learning of the target function. We then propose a mutual information based acquisition function that extends the predictive entropy principle. To overcome the computational challenges caused by large output dimensions, we use the multi-variate delta method and moment-matching to estimate the output posterior, and Weinstein-Aronszajn identity to calculate and optimize the acquisition function. We show the advantage of our method in several applications of computational physics and engineering design. The code is available at https://github.com/shib0li/DMFAL.

There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network one layer at a time with only a "single forward pass" has been proposed as an alternative to bypass BP; we refer to these networks as "layer-wise" networks. We continue the work on layer-wise networks by answering two outstanding questions. First, do they have a closed-form solution? Second, how do we know when to stop adding more layers? This work proves that the "Kernel Mean Embedding" is the closed-form solution that achieves the network global optimum while driving these networks to converge towards a highly desirable kernel for classification; we call it the Neural Indicator Kernel.

Multivariate time series anomaly detection has become an active area of research in recent years, with Deep Learning models outperforming previous approaches on benchmark datasets. Among reconstruction-based models, most previous work has focused on Variational Autoencoders and Generative Adversarial Networks. This work presents DGHL, a new family of generative models for time series anomaly detection, trained by maximizing the observed likelihood by posterior sampling and alternating back-propagation. A top-down Convolution Network maps a novel hierarchical latent space to time series windows, exploiting temporal dynamics to encode information efficiently. Despite relying on posterior sampling, it is computationally more efficient than current approaches, with up to 10x shorter training times than RNN based models. Our method outperformed current state-of-the-art models on four popular benchmark datasets. Finally, DGHL is robust to variable features between entities and accurate even with large proportions of missing values, settings with increasing relevance with the advent of IoT. We demonstrate the superior robustness of DGHL with novel occlusion experiments in this literature. Our code is available at https://github.com/cchallu/dghl.

Real-world time series data are often generated from several sources of variation. Learning representations that capture the factors contributing to this variability enables better understanding of the data via its underlying generative process and can lead to improvements in performance on downstream machine learning tasks. In this paper, we propose a novel generative approach for learning representations for the global and local factors of variation in time series data. The local representation of each sample models non-stationarity over time with a stochastic process prior, and the global representation of the sample encodes the time-independent characteristics. To encourage decoupling between the representations, we introduce a counterfactual regularization that minimizes the mutual information between the two variables. In experiments, we demonstrate successful recovery of the true local and global factors of variability on simulated data, and show that representations learned using our method lead to superior performance on downstream tasks on real-world datasets. We believe that the proposed way of defining representations is beneficial for data modelling and can yield better insights into the complexity of the real-world data.

It has been recently shown in the literature (Nie et al, 2018; Shin et al, 2019a,b) that the sample averages from online learning experiments are biased when used to estimate the mean reward. To correct the bias, off-policy evaluation methods, including importance sampling and doubly robust estimators, typically calculate the conditional propensity score, which is ill-defined for non-randomized policies such as UCB. This paper provides a procedure to debias the samples using bootstrap, which doesn’t require the knowledge of the reward distribution and can be applied to any adaptive policies. Numerical experiments demonstrate the effective bias reduction for samples generated by popular multi-armed bandit algorithms such as Explore-Then-Commit (ETC), UCB, Thompson sampling (TS) and $\epsilon$-greedy (EG). We analyze and provide theoretical justifications for the procedure under the ETC algorithm, including the asymptotic convergence of the bias decay rate in the real and bootstrap worlds.

While large training datasets generally offer improvement in model performance, the training process becomes computationally expensive and time consuming. Distributed learning is a common strategy to reduce the overall training time by exploiting multiple computing devices. Recently, it has been observed in the single machine setting that overparameterization is essential for benign overfitting in ridgeless regression in Hilbert spaces. We show that in this regime, data splitting has a regularizing effect, hence improving statistical performance and computational complexity at the same time. We further provide a unified framework that allows to analyze both the finite and infinite dimensional setting. We numerically demonstrate the effect of different model parameters.

One of the most effective approaches to improving the performance of a machine learning model is to procure additional training data. A model owner seeking relevant training data from a data owner needs to appraise the data before acquiring it. However, without a formal agreement, the data owner does not want to share data. The resulting Catch-22 prevents efficient data markets from forming. This paper proposes adding a data appraisal stage that requires no data sharing between data owners and model owners. Specifically, we use multi-party computation to implement an appraisal function computed on private data. The appraised value serves as a guide to facilitate data selection and transaction. We propose an efficient data appraisal method based on forward influence functions that approximates data value through its first-order loss reduction on the current model. The method requires no additional hyper-parameters or re-training. We show that in private, forward influence functions provide an appealing trade-off between high quality appraisal and required computation, in spite of label noise, class imbalance, and missing data. Our work seeks to inspire an open market that incentivizes efficient, equitable exchange of domain-specific training data.

Kernel Density Estimation (KDE) is a nonparametric method for estimatig the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor search, has been shown to enable fast KDE data structures. However, these approaches do not take advantage of the many other advances that have been made in algorithms for nearest neighbor algorithms. We present an algorithm called Density Estimation from Approximate Nearest Neighbors (DEANN) where we apply Approximate Nearest Neighbor (ANN) algorithms as a black box subroutine to compute an unbiased KDE. The idea is to find points that have a large contribution to the KDE using ANN, compute their contribution exactly, and approximate the remainder with Random Sampling (RS). We present a theoretical argument that supports the idea that an ANN subroutine can speed up the evaluation. Furthermore, we provide a C++ implementation with a Python interface that can make use of an arbitrary ANN implementation as a subroutine for KDE evaluation. We show empirically that our implementation outperforms state of the art implementations in all high dimensional datasets we considered, and matches the performance of RS in cases where the ANN yield no gains in performance.

Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence between data points is desired. Motivated to explicitly encode consistent bidirectional maps into the discrepancy measure, this work proposes a novel unbalanced Monge optimal transport formulation for matching, up to isometries, distributions on different spaces. Our formulation arises as a principled relaxation of the Gromov-Haussdroff distance between metric spaces, and employs two cycle-consistent maps that push forward each distribution onto the other. We study structural properties of the proposed discrepancy and, in particular, show that it captures the popular cycle-consistent generative adversarial network (GAN) framework as a special case, thereby providing the theory to explain it. Motivated by computational efficiency, we then kernelize the discrepancy and restrict the mappings to parametric function classes. The resulting kernelized version is coined the generalized maximum mean discrepancy (GMMD). Convergence rates for empirical estimation of GMMD are studied and experiments to support our theory are provided.

Merging the predictions of multiple experts is a frequent task. When ground-truth response values are available, this merging is often based on the estimated accuracies of the experts. In various applications, however, the only available information are the experts’ predictions on unlabeled test data, which do not allow to directly estimate their accuracies. Moreover, simple merging schemes such as majority voting in classification or the ensemble mean or median in regression, are clearly sub-optimal when some experts are more accurate than others. Focusing on regression tasks, in this work we propose U-PCR, a framework for unsupervised ensemble regression. Specifically, we develop spectral-based methods that under mild assumptions and in the absence of ground truth data, are able to estimate the mean squared error of the different experts and combine their predictions to a more accurate meta-learner. We provide theoretical support for U-PCR as well as empirical evidence for the validity of its underlying assumptions. On a variety of regression problems, we illustrate the improved accuracy of U-PCR over various unsupervised merging strategies. Finally, we also illustrate its applicability to unsupervised multi-class ensemble learning.

As machine learning is increasingly deployed in the real world, it is paramount that we develop the tools necessary to analyze the decision-making of the models we train and deploy to end-users. Recently, researchers have shown that influence functions, a statistical measure of sample impact, can approximate the effects of training samples on classification accuracy for deep neural networks. However, this prior work only applies to supervised learning, where training and testing share an objective function. No approaches currently exist for estimating the influence of unsupervised training examples for deep learning models. To bring explainability to unsupervised and semi-supervised training regimes, we derive the first theoretical and empirical demonstration that influence functions can be extended to handle mismatched training and testing (i.e., "cross-loss") settings. Our formulation enables us to compute the influence in an unsupervised learning setup, explain cluster memberships, and identify and augment biases in language models. Our experiments show that our cross-loss influence estimates even exceed matched-objective influence estimation relative to ground-truth sample impact.

Counterfactual Explanation (CE) is a post-hoc explanation method that provides a perturbation for altering the prediction result of a classifier. An individual can interpret the perturbation as an "action" to obtain the desired decision results. Existing CE methods focus on providing an action, which is optimized for a given single instance. However, these CE methods do not address the case where we have to assign actions to multiple instances simultaneously. In such a case, we need a framework of CE that assigns actions to multiple instances in a transparent and consistent way. In this study, we propose Counterfactual Explanation Tree (CET) that assigns effective actions with decision trees. Due to the properties of decision trees, our CET has two advantages: (1) Transparency: the reasons for assigning actions are summarized in an interpretable structure, and (2) Consistency: these reasons do not conflict with each other. We learn a CET in two steps: (i) compute one effective action for multiple instances and (ii) partition the instances to balance the effectiveness and interpretability. Numerical experiments and user studies demonstrated the efficacy of our CET in comparison with existing methods.

We study the adversarial robustness in offline reinforcement learning. Given a batch dataset consisting of tuples $(s, a, r, s’)$, an adversary is allowed to arbitrarily modify $\epsilon$ fraction of the tuples. From the corrupted dataset the learner aims to robustly identify a near-optimal policy. We first show that a worst-case $\Omega(d\epsilon)$ optimality gap is unavoidable in linear MDP of dimension $d$, even if the adversary only corrupts the reward element in a tuple. This contrasts with dimension-free results in robust supervised learning and best-known lower-bound in the online RL setting with corruption. Next, we propose robust variants of the Least-Square Value Iteration (LSVI) algorithm utilizing robust supervised learning oracles, which achieve near-matching performances in cases both with and without full data coverage. The algorithm requires the knowledge of $\epsilon$ to design the pessimism bonus in the no-coverage case. Surprisingly, in this case, the knowledge of $\epsilon$ is necessary, as we show that being adaptive to unknown $\epsilon$ is impossible. This again contrasts with recent results on corruption-robust online RL and implies that robust offline RL is a strictly harder problem.

In the monitoring problem, the input is an unbounded stream $P={p_1,p_2\cdots}$ of integers in $[N]:=\{1,\cdots,N\}$, that are obtained from a sensor (such as GPS or heart beats of a human). The goal (e.g., for anomaly detection) is to approximate the $n$ points received so far in $P$ by a single frequency $\sin$, e.g. $\min_{c\in C}cost(P,c)+\lambda(c)$, where $cost(P,c)=\sum_{i=1}^n \sin^2(\frac{2\pi}{N} p_ic)$, $C\subseteq [N]$ is a feasible set of solutions, and $\lambda$ is a given regularization function. For any approximation error $\varepsilon>0$, we prove that every set $P$ of $n$ integers has a weighted subset $S\subseteq P$ (sometimes called core-set) of cardinality $|S|\in O(\log(N)^{O(1)})$ that approximates $cost(P,c)$ (for every $c\in [N]$) up to a multiplicative factor of $1\pm\varepsilon$. Using known coreset techniques, this implies streaming algorithms using only $O((\log(N)\log(n))^{O(1)})$ memory. Our results hold for a large family of functions. Experimental results and open source code are provided.

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the convergence property of the dynamics is of great theoretical interest. In this work, we give a concise and self-contained convergence rate analysis of the mean field Langevin dynamics with respect to the (regularized) objective function in both continuous and discrete time settings. The key ingredient of our proof is a proximal Gibbs distribution $p_q$ associated with the dynamics, which, in combination with techniques in Vempala and Wibisono (2019), allows us to develop a simple convergence theory parallel to classical results in convex optimization. Furthermore, we reveal that $p_q$ connects to the duality gap in the empirical risk minimization setting, which enables efficient empirical evaluation of the algorithm convergence.

Non-convex sparse regularizers are common tools for learning with high-dimensional data. For accelerating convergence for Lasso problem involving those regularizers, a working set strategy addresses the optimization problem through an iterative algorithm by gradually incrementing the number of variables to optimize until the identification of the solution support. We propose in this paper the first Lasso working set algorithm for non-convex sparse regularizers with convergence guarantees. The algorithm, named FireWorks, is based on a non-convex reformulation of a recent duality-based approach and leverages on the geometry of the residuals. We provide theoretical guarantees showing that convergence is preserved even when the inner solver is inexact, under sufficient decay of the error across iterations. Experimental results demonstrate strong computational gain when using our working set strategy compared to full problem solvers for both block-coordinate descent or a proximal gradient solver.

We prove asymptotic convergence for a general class of k-means algorithms performed over streaming data from a distribution–the centers asymptotically converge to the set of stationary points of the k-means objective function. To do so, we show that online k-means over a distribution can be interpreted as stochastic gradient descent with a stochastic learning rate schedule. Then, we prove convergence by extending techniques used in optimization literature to handle settings where center-specific learning rates may depend on the past trajectory of the centers.

We study sampling from a target distribution $\nu_* = e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential $f$ satisfies a strong dissipativity condition and it is first-order smooth with a Lipschitz gradient. We prove that, initialized with a Gaussian random vector that has sufficiently small variance, iterating the LMC algorithm for $\widetilde{\mathcal{O}}(\lambda^2 d\epsilon^{-1})$ steps is sufficient to reach $\epsilon$-neighborhood of the target in both Chi-squared and Rényi divergence, where $\lambda$ is the logarithmic Sobolev constant of $\nu_*$. Our results do not require warm-start to deal with the exponential dimension dependency in Chi-squared divergence at initialization. In particular, for strongly convex and first-order smooth potentials, we show that the LMC algorithm achieves the rate estimate $\widetilde{\mathcal{O}}(d\epsilon^{-1})$ which improves the previously known rates in both of these metrics, under the same assumptions. Translating this rate to other metrics, our results also recover the state-of-the-art rate estimates in KL divergence, total variation and $2$-Wasserstein distance in the same setup. Finally, as we rely on the logarithmic Sobolev inequality, our framework covers a range of non-convex potentials that are first-order smooth and exhibit strong convexity outside of a compact region.