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We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel&#39;s Mercer expansion. In particular, we bound the Kullbackâ€“Leibler divergence between an exact GP and one resulting from one of the afore-described low-rank approximations to its 
 kernel, as well as between their corresponding predictive densities, and we also bound the error between predictive mean vectors and between predictive covariance matrices computed using the exact versus using the approximate GP. We provide experiments on both simulated data and standard benchmarks to evaluate the effectiveness of our theoretical bounds.

AAAI 2022

How Good Are Low-Rank Approximations in Gaussian Process Regression?

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2021

We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we bound the Kullbackâ€“Leibler divergence between an exact GP and one resulting from one of the afore-described low-rank approximations to its 
 kernel, as well as between their corresponding predictive densities, and we also bound the error between predictive mean vectors and between predictive covariance matrices computed using the exact versus using the approximate GP. We provide experiments on both simulated data and standard benchmarks to evaluate the effectiveness of our theoretical bounds.

technical paper

Few-shot classification requires adapting knowledge learned from a large annotated base dataset to recognize novel unseen classes, each represented by few labeled examples. In such a scenario, pretraining a network with high capacity on the large dataset and then finetuning it on the few examples causes severe overfitting. At the same time, training a simple linear classifier on top of ``frozen'' features learned from the large labeled dataset fails to adapt the model to the properties of the novel classes, effectively inducing underfitting. In this paper we propose an alternative approach to both of these two popular strategies. First, our method pseudo-labels the entire large dataset using the linear classifier trained on the novel classes. This effectively ``hallucinates'' the novel classes in the large dataset, despite the novel categories not being present in the base database (novel and base classes are disjoint). Then, it finetunes the entire model with a distillation loss on the pseudo-labeled base examples, in addition to the standard cross-entropy loss on the novel dataset. This step effectively trains the network to recognize contextual and appearance cues that are useful for the novel-category recognition but using the entire large-scale base dataset and thus overcoming the inherent data-scarcity problem of few-shot learning. Despite the simplicity of the approach, we show that that our method outperforms the state-of-the-art on four well-established few-shot classification benchmarks. The code is available at https://github.com/yiren-jian/LabelHalluc.

Label Hallucination for Few-Shot Classification

In this paper, we tackle the problem of one-shot unsupervised domain adaptation (OSUDA) for semantic segmentation where the segmentors only see one unlabeled target image during training. In this case, traditional unsupervised domain adaptation models usually fail since they cannot adapt to the target domain with over-fitting to one (or few) target samples. To address this problem, existing OSUDA methods usually integrate a style-transfer module to perform domain randomization based on the unlabeled target sample, with which multiple domains around the target sample can be explored during training. However, such a style-transfer module relies on an additional set of images as style reference for pre-training and also increases the memory demand for domain adaptation. Here we propose a new OSUDA method that can effectively relieve such computational burden. Specifically, we integrate several style-mixing layers into the segmentor which play the role of style-transfer module to stylize the source images without introducing any learned parameters. Moreover, we propose a patchwise prototypical matching (PPM) method to weighted consider the importance of source pixels during the supervised training to relieve the negative adaptation. Experimental results show that our method achieves new state-of-the-art performance on two commonly used benchmarks for domain adaptive semantic segmentation under the one-shot setting and is more efficient than all comparison approaches.

Style Mixing and Patchwise Prototypical Matching for One-Shot Unsupervised Domain Adaptive Semantic Segmentation

In Apprenticeship Learning (AL), we are given a Markov Decision Process (MDP) without access to the cost function. Instead, we observe trajectories sampled by an expert that acts according to some policy. The goal is to find a policy that matches the expert's performance on some predefined set of cost functions. 
We introduce an online variant of AL (Online Apprenticeship Learning; OAL), where the agent is expected to perform comparably to the expert while interacting with the environment. We show that the OAL problem can be effectively solved by combining two mirror descent based no-regret algorithms: one for policy optimization and another for learning the worst case cost. By employing optimistic exploration, we derive a convergent algorithm with O(sqrt(K)) regret, where K is the number of interactions with the MDP, and an additional linear error term that depends on the amount of expert trajectories available. Importantly, our algorithm avoids the need to solve an MDP at each iteration, making it more practical compared to prior AL methods. Finally, we implement a deep variant of our algorithm which shares some similarities to GAIL, but where the discriminator is replaced with the costs learned by OAL. Our simulations suggest that OAL performs well in high dimensional control problems.

Online Apprenticeship Learning

This paper starts by revealing a surprising finding: without any learning, a randomly initialized CNN can localize objects surprisingly well. That is, a CNN has an inductive bias to naturally focus on objects, named as Tobias ("The object is at sight") in this paper. This empirical inductive bias is further analyzed and successfully applied to self-supervised learning (SSL). A CNN is encouraged to learn representations that focus on the foreground object, by transforming every image into various versions with different backgrounds, where the foreground and background separation is guided by Tobias. Experimental results show that the proposed Tobias significantly improves downstream tasks, especially for object detection. This paper also shows that Tobias has consistent improvements on training sets of different sizes, and is more resilient to changes in image augmentations.

A Random CNN Sees Objects: One Inductive Bias of CNN and Its Applications

We study regret minimization in finite horizon tabular Markov decision processes (MDPs) under the constraints of differential privacy (DP). This is motivated by the widespread applications of reinforcement learning (RL) in real-world sequential decision making problems, where protecting users' sensitive and private information is becoming paramount. We consider two variants of DP -- joint DP (JDP), where a centralized agent is responsible for protecting users' sensitive data and local DP (LDP), where information needs to be protected directly on the user side. We first propose two general frameworks -- one for policy optimization and another for value iteration -- for designing private, optimistic RL algorithms. We then instantiate these frameworks with suitable privacy mechanisms to satisfy JDP and LDP requirements, and simultaneously obtain sublinear regret guarantees. The regret bounds show that under JDP, the cost of privacy is only a lower order additive term, while for a stronger privacy protection under LDP, the cost suffered is multiplicative. Finally, the regret bounds are obtained by a unified analysis, which, we believe, can be extended beyond tabular MDPs.

Differentially Private Regret Minimization in Episodic Markov Decision Processes

With ever-increasing dataset sizes, subset selection techniques are becoming increasingly important for a plethora of tasks. It is often necessary to guide the subset selection to achieve certain desiderata, which includes focusing or targeting certain data points, while avoiding others. Examples of such problems include: i)targeted learning, where the goal is to find subsets with rare classes or rare attributes on which the model is under performing, and ii)guided summarization, where data (e.g., image collection, text, document or video) is summarized for quicker human consumption with specific additional user intent. Motivated by such applications, we present PRISM, a rich class of PaRameterIzed Submodular information Measures. Through novel functions and their parameterizations, PRISM offers a variety of modeling capabilities that enable a trade-off between desired qualities of a subset like diversity or representation and similarity/dissimilarity with a set of data points. We demonstrate how PRISM can be applied to the two real-world problems mentioned above, which require guided subset selection. In doing so, we show that PRISM interestingly generalizes some past work, therein reinforcing its broad utility. Through extensive experiments on diverse datasets, we demonstrate the superiority of PRISM over the state-of-the-art in targeted learning and in guided image-collection summarization. PRISM is available as a part of the SUBMODLIB (https://github.com/decile-team/submodlib) and TRUST (https://github.com/decile-team/trust) toolkits.

PRISM: A Rich Class of Parameterized Submodular Information Measures for Guided Data Subset Selection

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search methods can find the ground truth with a small error. By analyzing the landscape of the non-convex problem, we first propose a global guarantee on the maximum distance between an arbitrary local minimizer and the ground truth under the assumption that the RIP constant is smaller than 1/2. We show that this distance shrinks to zero as the intensity of the noise reduces. Our new guarantee is sharp in terms of the RIP constant and is much stronger than the existing results. We then present a local guarantee for problems with an arbitrary RIP constant, which states that any local minimizer is either considerably close to the ground truth or far away from it. Next, we prove the strict saddle property, which guarantees the global convergence of the perturbed gradient descent method in polynomial time. The developed results demonstrate how the noise intensity and the RIP constant of the problem affect the landscape of the problem.

Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements

Transformers have become one of the dominant architectures in deep learning, particularly as a powerful alternative to convolutional neural networks (CNNs) in computer vision. However, Transformer training and inference in previous works can be prohibitively expensive due to the quadratic complexity of self-attention over a long sequence of representations, especially for high-resolution dense prediction tasks. To this end, we present a novel Less attention vIsion Transformer (LIT), building upon the fact that the early self-attention layers in Transformers still focus on local patterns and bring minor benefits in recent hierarchical vision Transformers. Specifically, we propose a hierarchical Transformer where we use pure multi-layer perceptrons (MLPs) to encode rich local patterns in the early stages while applying self-attention modules to capture longer dependencies in deeper layers. Moreover, we further propose a learned deformable token merging module to adaptively fuse informative patches in a non-uniform manner. The proposed LIT achieves promising performance on image recognition tasks, including image classification, object detection and instance segmentation, serving as a strong backbone for many vision tasks. Code is available at https://github.com/zip-group/LIT.

Less is More: Pay Less Attention in Vision Transformers

Text revision refers to a family of natural language generation tasks, where the source and target sequences share moderate resemblance in surface form but differentiate in attributes, such as text formality and simplicity. Current state-of-the-art methods formulate these tasks as sequence-to-sequence learning problems, which rely on large-scale parallel training corpus. In this paper, we present an iterative in-place editing approach for text revision, which requires no parallel data. In this approach, we simply fine-tune a pre-trained Transformer with masked language modeling and attribute classification. During inference, the editing at each iteration is realized by two-step span replacement. At the first step, the distributed representation of the text optimizes on the fly towards an attribute function. At the second step, a text span is masked and another new one is proposed conditioned on the optimized representation. The empirical experiments on two typical and important text revision tasks, text formalization and text simplification, show the effectiveness of our approach. It achieves competitive and even better performance than state-of-the-art supervised methods on text simplification, and gains better performance than strong unsupervised methods on text formalization. Our code and model are released at https://github.com/jingjingli01/OREO.

Text Revision by On-the-Fly Representation Optimization

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fair-ness criteria at the group and individual level, whichâ€”unlike prior work on equalising the average group-wise distance from the decision boundaryâ€”explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

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