Hongjian Wang

Ben Chugg, Hongjian Wang, Aaditya Ramdas · cmu

We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike most previous literature on this topic, our bounds are anytime-valid (i.e., time-uniform), meaning that they hold at all stopping times, not only for a fixed sample size. Our approach combines four tools in the following order: (a) nonnegative supermartingales or reverse submartingales, (b) the method of mixtures, (c) the Donsker-Varadhan formula (or other convex duality principles), and (d) Ville's inequality. Our main result is a PAC-Bayes theorem which holds for a wide class of discrete stochastic processes. We show how this result implies time-uniform versions of well-known classical PAC-Bayes bounds, such as those of Seeger, McAllester, Maurer, and Catoni, in addition to many recent bounds. We also present several novel bounds. Our framework also enables us to relax traditional assumptions; in particular, we consider nonstationary loss functions and non-i.i.d. data. In sum, we unify the derivation of past bounds and ease the search for future bounds: one may simply check if our supermartingale or submartingale conditions are met and, if so, be guaranteed a (time-uniform) PAC-Bayes bound.

Hongjian Wang, Aaditya Ramdas · cmu

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the $p$-th central moment ($p$ > 1), but allowing for (at most) $ε$ fraction of arbitrary distribution corruption, as in Huber's contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.

Hongjian Wang, Aaditya Ramdas · cmu

In 1976, Lai constructed a nontrivial confidence sequence for the mean $μ$ of a Gaussian distribution with unknown variance $σ^2$. Curiously, he employed both an improper (right Haar) mixture over $σ$ and an improper (flat) mixture over $μ$. Here, we elaborate carefully on the details of his construction, which use generalized nonintegrable martingales and an extended Ville's inequality. While this does yield a sequential t-test, it does not yield an "e-process" (due to the nonintegrability of his martingale). In this paper, we develop two new e-processes and confidence sequences for the same setting: one is a test martingale in a reduced filtration, while the other is an e-process in the canonical data filtration. These are respectively obtained by swapping Lai's flat mixture for a Gaussian mixture, and swapping the right Haar mixture over $σ$ with the maximum likelihood estimate under the null, as done in universal inference. We also analyze the width of resulting confidence sequences, which have a curious polynomial dependence on the error probability $α$ that we prove to be not only unavoidable, but (for universal inference) even better than the classical fixed-sample t-test. Numerical experiments are provided along the way to compare and contrast the various approaches, including some recent suboptimal ones.

Yunfan Lu, Zipeng Wang, Minjie Liu et al.

Event cameras sense the intensity changes asynchronously and produce event streams with high dynamic range and low latency. This has inspired research endeavors utilizing events to guide the challenging video superresolution (VSR) task. In this paper, we make the first attempt to address a novel problem of achieving VSR at random scales by taking advantages of the high temporal resolution property of events. This is hampered by the difficulties of representing the spatial-temporal information of events when guiding VSR. To this end, we propose a novel framework that incorporates the spatial-temporal interpolation of events to VSR in a unified framework. Our key idea is to learn implicit neural representations from queried spatial-temporal coordinates and features from both RGB frames and events. Our method contains three parts. Specifically, the Spatial-Temporal Fusion (STF) module first learns the 3D features from events and RGB frames. Then, the Temporal Filter (TF) module unlocks more explicit motion information from the events near the queried timestamp and generates the 2D features. Lastly, the SpatialTemporal Implicit Representation (STIR) module recovers the SR frame in arbitrary resolutions from the outputs of these two modules. In addition, we collect a real-world dataset with spatially aligned events and RGB frames. Extensive experiments show that our method significantly surpasses the prior-arts and achieves VSR with random scales, e.g., 6.5. Code and dataset are available at https: //vlis2022.github.io/cvpr23/egvsr.

Chunqing Ruan, Hongjian Wang

Parameter efficient transfer learning (PETL) is an emerging research spot that aims to adapt large-scale pre-trained models to downstream tasks. Recent advances have achieved great success in saving storage and computation costs. However, these methods do not take into account instance-specific visual clues for visual tasks. In this paper, we propose a Dynamic Visual Prompt Tuning framework (DVPT), which can generate a dynamic instance-wise token for each image. In this way, it can capture the unique visual feature of each image, which can be more suitable for downstream visual tasks. We designed a Meta-Net module that can generate learnable prompts based on each image, thereby capturing dynamic instance-wise visual features. Extensive experiments on a wide range of downstream recognition tasks show that DVPT achieves superior performance than other PETL methods. More importantly, DVPT even outperforms full fine-tuning on 17 out of 19 downstream tasks while maintaining high parameter efficiency. Our code will be released soon.

Hongjian Wang, Mert Gürbüzbalaban, Lingjiong Zhu et al.

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging variance, which hinders the use of conventional convergence analysis techniques that rely on the existence of the second-order moments. In this paper, we provide convergence guarantees for SGD under a state-dependent and heavy-tailed noise with a potentially infinite variance, for a class of strongly convex objectives. In the case where the $p$-th moment of the noise exists for some $p\in [1,2)$, we first identify a condition on the Hessian, coined '$p$-positive (semi-)definiteness', that leads to an interesting interpolation between positive semi-definite matrices ($p=2$) and diagonally dominant matrices with non-negative diagonal entries ($p=1$). Under this condition, we then provide a convergence rate for the distance to the global optimum in $L^p$. Furthermore, we provide a generalized central limit theorem, which shows that the properly scaled Polyak-Ruppert averaging converges weakly to a multivariate $α$-stable random vector. Our results indicate that even under heavy-tailed noise with infinite variance, SGD can converge to the global optimum without necessitating any modification neither to the loss function or to the algorithm itself, as typically required in robust statistics. We demonstrate the implications of our results to applications such as linear regression and generalized linear models subject to heavy-tailed data.

Hongjian Wang, Qi Li, Lanbo Zhang et al.

Historical features are important in ads click-through rate (CTR) prediction, because they account for past engagements between users and ads. In this paper, we study how to efficiently construct historical features through counting features. The key challenge of such problem lies in how to automatically identify counting keys. We propose a tree-based method for counting key selection. The intuition is that a decision tree naturally provides various combinations of features, which could be used as counting key candidate. In order to select personalized counting features, we train one decision tree model per user, and the counting keys are selected across different users with a frequency-based importance measure. To validate the effectiveness of proposed solution, we conduct large scale experiments on Twitter video advertising data. In both online learning and offline training settings, the automatically identified counting features outperform the manually curated counting features.

Guanjie Zheng, Mengqi Liu, Tao Wen et al.

In the face of growing needs for water and energy, a fundamental understanding of the environmental impacts of human activities becomes critical for managing water and energy resources, remedying water pollution, and making regulatory policy wisely. Among activities that impact the environment, oil and gas production, wastewater transport, and urbanization are included. In addition to the occurrence of anthropogenic contamination, the presence of some contaminants (e.g., methane, salt, and sulfate) of natural origin is not uncommon. Therefore, scientists sometimes find it difficult to identify the sources of contaminants in the coupled natural and human systems. In this paper, we propose a technique to simultaneously conduct source detection and prediction, which outperforms other approaches in the interdisciplinary case study of the identification of potential groundwater contamination within a region of high-density shale gas development.

Hongjian Wang, Zhenhui Li, Yu-Hsuan Kuo et al.

The increased availability of large-scale trajectory data around the world provides rich information for the study of urban dynamics. For example, New York City Taxi Limousine Commission regularly releases source-destination information about trips in the taxis they regulate. Taxi data provide information about traffic patterns, and thus enable the study of urban flow -- what will traffic between two locations look like at a certain date and time in the future? Existing big data methods try to outdo each other in terms of complexity and algorithmic sophistication. In the spirit of "big data beats algorithms", we present a very simple baseline which outperforms state-of-the-art approaches, including Bing Maps and Baidu Maps (whose APIs permit large scale experimentation). Such a travel time estimation baseline has several important uses, such as navigation (fast travel time estimates can serve as approximate heuristics for A search variants for path finding) and trip planning (which uses operating hours for popular destinations along with travel time estimates to create an itinerary).