Statistical Inference with Stochastic Gradient Methods under $φ$-mixing Data

Stochastic gradient descent (SGD) is a scalable and memory-efficient optimization algorithm for large datasets and stream data, which has drawn a great deal of attention and popularity. The applications of SGD-based estimators to statistical inference such as interval estimation have also achieved great success. However, most of the related works are based on i.i.d. observations or Markov chains. When the observations come from a mixing time series, how to conduct valid statistical inference remains unexplored. As a matter of fact, the general correlation among observations imposes a challenge on interval estimation. Most existing methods may ignore this correlation and lead to invalid confidence intervals. In this paper, we propose a mini-batch SGD estimator for statistical inference when the data is $\phi$-mixing. The confidence intervals are constructed using an associated mini-batch bootstrap SGD procedure. Using ``independent block'' trick from \cite{yu1994rates}, we show that the proposed estimator is asymptotically normal, and its limiting distribution can be effectively approximated by the bootstrap procedure. The proposed method is memory-efficient and easy to implement in practice. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.

Uniformity Testing over Hypergrids with Subcube Conditioning

We give an algorithm for testing uniformity of distributions supported on hypergrids $[m]^n$, which makes $\tilde{O}(\text{poly}(m)\sqrt{n}/\epsilon^2)$ queries to a subcube conditional sampling oracle. When the side length $m$ of the hypergrid is a constant, our algorithm is nearly optimal and strengthens the algorithm of [CCK+21] which has the same query complexity but works for hypercubes $\{\pm 1\}^n$ only. A key technical contribution behind the analysis of our algorithm is a proof of a robust version of Pisier's inequality for functions over $\mathbb{Z}_m^n$ using Fourier analysis.

Vision, Deduction and Alignment: An Empirical Study on Multi-modal Knowledge Graph Alignment

Entity alignment (EA) for knowledge graphs (KGs) plays a critical role in knowledge engineering. Existing EA methods mostly focus on utilizing the graph structures and entity attributes (including literals), but ignore images that are common in modern multi-modal KGs. In this study we first constructed Multi-OpenEA -- eight large-scale, image-equipped EA benchmarks, and then evaluated some existing embedding-based methods for utilizing images. In view of the complementary nature of visual modal information and logical deduction, we further developed a new multi-modal EA method named LODEME using logical deduction and multi-modal KG embedding, with state-of-the-art performance achieved on Multi-OpenEA and other existing multi-modal EA benchmarks.

3D Molecular Generation via Virtual Dynamics

Structure-based drug design, i.e., finding molecules with high affinities to the target protein pocket, is one of the most critical tasks in drug discovery. Traditional solutions, like virtual screening, require exhaustively searching on a large molecular database, which are inefficient and cannot return novel molecules beyond the database. The pocket-based 3D molecular generation model, i.e., directly generating a molecule with a 3D structure and binding position in the pocket, is a new promising way to address this issue. Herein, we propose VD-Gen, a novel pocket-based 3D molecular generation pipeline. VD-Gen consists of several carefully designed stages to generate fine-grained 3D molecules with binding positions in the pocket cavity end-to-end. Rather than directly generating or sampling atoms with 3D positions in the pocket like in early attempts, in VD-Gen, we first randomly initialize many virtual particles in the pocket; then iteratively move these virtual particles, making the distribution of virtual particles approximate the distribution of molecular atoms. After virtual particles are stabilized in 3D space, we extract a 3D molecule from them. Finally, we further refine atoms in the extracted molecule by iterative movement again, to get a high-quality 3D molecule, and predict a confidence score for it. Extensive experiment results on pocket-based molecular generation demonstrate that VD-Gen can generate novel 3D molecules to fill the target pocket cavity with high binding affinities, significantly outperforming previous baselines.

Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models

Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.

Inference on the Optimal Assortment in the Multinomial Logit Model

Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.

Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent

With the fast development of big data, it has been easier than before to learn the optimal decision rule by updating the decision rule recursively and making online decisions. We study the online statistical inference of model parameters in a contextual bandit framework of sequential decision-making. We propose a general framework for online and adaptive data collection environment that can update decision rules via weighted stochastic gradient descent. We allow different weighting schemes of the stochastic gradient and establish the asymptotic normality of the parameter estimator. Our proposed estimator significantly improves the asymptotic efficiency over the previous averaged SGD approach via inverse probability weights. We also conduct an optimality analysis on the weights in a linear regression setting. We provide a Bahadur representation of the proposed estimator and show that the remainder term in the Bahadur representation entails a slower convergence rate compared to classical SGD due to the adaptive data collection.

Hyperspherical Quantization: Toward Smaller and More Accurate Models

Model quantization enables the deployment of deep neural networks under resource-constrained devices. Vector quantization aims at reducing the model size by indexing model weights with full-precision embeddings, i.e., codewords, while the index needs to be restored to 32-bit during computation. Binary and other low-precision quantization methods can reduce the model size up to 32$\times$, however, at the cost of a considerable accuracy drop. In this paper, we propose an efficient framework for ternary quantization to produce smaller and more accurate compressed models. By integrating hyperspherical learning, pruning and reinitialization, our proposed Hyperspherical Quantization (HQ) method reduces the cosine distance between the full-precision and ternary weights, thus reducing the bias of the straight-through gradient estimator during ternary quantization. Compared with existing work at similar compression levels ($\sim$30$\times$, $\sim$40$\times$), our method significantly improves the test accuracy and reduces the model size.

FreeEnricher: Enriching Face Landmarks without Additional Cost

Recent years have witnessed significant growth of face alignment. Though dense facial landmark is highly demanded in various scenarios, e.g., cosmetic medicine and facial beautification, most works only consider sparse face alignment. To address this problem, we present a framework that can enrich landmark density by existing sparse landmark datasets, e.g., 300W with 68 points and WFLW with 98 points. Firstly, we observe that the local patches along each semantic contour are highly similar in appearance. Then, we propose a weakly-supervised idea of learning the refinement ability on original sparse landmarks and adapting this ability to enriched dense landmarks. Meanwhile, several operators are devised and organized together to implement the idea. Finally, the trained model is applied as a plug-and-play module to the existing face alignment networks. To evaluate our method, we manually label the dense landmarks on 300W testset. Our method yields state-of-the-art accuracy not only in newly-constructed dense 300W testset but also in the original sparse 300W and WFLW testsets without additional cost.

Interpretable Node Representation with Attribute Decoding

Variational Graph Autoencoders (VGAEs) are powerful models for unsupervised learning of node representations from graph data. In this work, we systematically analyze modeling node attributes in VGAEs and show that attribute decoding is important for node representation learning. We further propose a new learning model, interpretable NOde Representation with Attribute Decoding (NORAD). The model encodes node representations in an interpretable approach: node representations capture community structures in the graph and the relationship between communities and node attributes. We further propose a rectifying procedure to refine node representations of isolated notes, improving the quality of these nodes' representations. Our empirical results demonstrate the advantage of the proposed model when learning graph data in an interpretable approach.