OpenRaiser/Intern-Atlas huggingface dataset:
Leveraged Matrix Completion with Noise
Venue: arXiv cs.LG 2023
Year: 2023

Completing low-rank matrices from subsampled measurements has received much attention in the past decade. Existing works indicate that $\mathcal{O}(nr\log^2(n))$ datums are required to theoretically secure the completion of an $n \times n$ noisy matrix of rank $r$ with high probability, under some quite restrictive assumptions: (1) the underlying matrix must be incoherent; (2) observations follow the uniform distribution. The restrictiveness is partially due to ignoring the roles of the leverage score and the oracle information of each element. In this paper, we employ the leverage scores to characterize the importance of each element and significantly relax assumptions to: (1) not any other structure assumptions are imposed on the underlying low-rank matrix; (2) elements being observed are appropriately dependent on their importance via the leverage score. Under these assumptions, instead of uniform sampling, we devise an ununiform/biased sampling procedure that can reveal the ``importance'' of each observed element. Our proofs are supported by a novel approach that phrases sufficient optimality conditions based on the Golfing Scheme, which would be of independent interest to the wider areas. Theoretical findings show that we can provably recover an unknown $n\times n$ matrix of rank $r$ from just about $\mathcal{O}(nr\log^2 (n))$ entries, even when the observed entries are corrupted with a small amount of noisy information. The empirical results align precisely with our theories.
A New Bandit Setting Balancing Information from State Evolution and Corrupted Context
Venue: arXiv cs.LG 2023
Year: 2023

We propose a new sequential decision-making setting, combining key aspects of two established online learning problems with bandit feedback. The optimal action to play at any given moment is contingent on an underlying changing state which is not directly observable by the agent. Each state is associated with a context distribution, possibly corrupted, allowing the agent to identify the state. Furthermore, states evolve in a Markovian fashion, providing useful information to estimate the current state via state history. In the proposed problem setting, we tackle the challenge of deciding on which of the two sources of information the agent should base its arm selection. We present an algorithm that uses a referee to dynamically combine the policies of a contextual bandit and a multi-armed bandit. We capture the time-correlation of states through iteratively learning the action-reward transition model, allowing for efficient exploration of actions. Our setting is motivated by adaptive mobile health (mHealth) interventions. Users transition through different, time-correlated, but only partially observable internal states, determining their current needs. The side information associated with each internal state might not always be reliable, and standard approaches solely rely on the context risk of incurring high regret. Similarly, some users might exhibit weaker correlations between subsequent states, leading to approaches that solely rely on state transitions risking the same. We analyze our setting and algorithm in terms of regret lower bound and upper bounds and evaluate our method on simulated medication adherence intervention data and several real-world data sets, showing improved empirical performance compared to several popular algorithms.
Normalized Weighting Schemes for Image Interpolation Algorithms
Venue: arXiv cs.GR 2023
Year: 2023

Image interpolation algorithms pervade many modern image processing and analysis applications. However, when their weighting schemes inefficiently generate very unrealistic estimates, they may negatively affect the performance of the end user applications. Therefore, in this work, the author introduced four weighting schemes based on some geometric shapes for digital image interpolation operations. And, the quantity used to express the extent of each shape weight was the normalized area, especially when the sums of areas exceeded a unit square size. The introduced four weighting schemes are based on the minimum side based diameter (MD) of a regular tetragon, hypotenuse based radius (HR), the virtual pixel length based height for the area of the triangle (AT), and the virtual pixel length for hypotenuse based radius for the area of the circle (AC). At the smaller scaling ratio, the image interpolation algorithm based on the HR scheme scored the highest at 66.6 % among non traditional image interpolation algorithms presented. But, at the higher scaling ratio, the AC scheme based image interpolation algorithm scored the highest at 66.6 % among non traditional algorithms presented and, here, its image interpolation quality was generally superior or comparable to the quality of images interpolated by both non traditional and traditional algorithms.
Deep Serial Number: Computational Watermarking for DNN Intellectual Property Protection
Venue: arXiv cs.CR 2023
Year: 2023

In this paper, we present DSN (Deep Serial Number), a simple yet effective watermarking algorithm designed specifically for deep neural networks (DNNs). Unlike traditional methods that incorporate identification signals into DNNs, our approach explores a novel Intellectual Property (IP) protection mechanism for DNNs, effectively thwarting adversaries from using stolen networks. Inspired by the success of serial numbers in safeguarding conventional software IP, we propose the first implementation of serial number embedding within DNNs. To achieve this, DSN is integrated into a knowledge distillation framework, in which a private teacher DNN is initially trained. Subsequently, its knowledge is distilled and imparted to a series of customized student DNNs. Each customer DNN functions correctly only upon input of a valid serial number. Experimental results across various applications demonstrate DSN's efficacy in preventing unauthorized usage without compromising the original DNN performance. The experiments further show that DSN is resistant to different categories of watermark attacks.
UP-DETR: Unsupervised Pre-training for Object Detection with Transformers
Venue: arXiv cs.CV 2023
Year: 2023

DEtection TRansformer (DETR) for object detection reaches competitive performance compared with Faster R-CNN via a transformer encoder-decoder architecture. However, trained with scratch transformers, DETR needs large-scale training data and an extreme long training schedule even on COCO dataset. Inspired by the great success of pre-training transformers in natural language processing, we propose a novel pretext task named random query patch detection in Unsupervised Pre-training DETR (UP-DETR). Specifically, we randomly crop patches from the given image and then feed them as queries to the decoder. The model is pre-trained to detect these query patches from the input image. During the pre-training, we address two critical issues: multi-task learning and multi-query localization. (1) To trade off classification and localization preferences in the pretext task, we find that freezing the CNN backbone is the prerequisite for the success of pre-training transformers. (2) To perform multi-query localization, we develop UP-DETR with multi-query patch detection with attention mask. Besides, UP-DETR also provides a unified perspective for fine-tuning object detection and one-shot detection tasks. In our experiments, UP-DETR significantly boosts the performance of DETR with faster convergence and higher average precision on object detection, one-shot detection and panoptic segmentation. Code and pre-training models: https://github.com/dddzg/up-detr.
Searching, Sorting, and Cake Cutting in Rounds
Venue: arXiv cs.DS 2023
Year: 2023

We study searching and sorting in rounds motivated by a fair division question: given a cake cutting problem with $n$ players, compute a fair allocation in at most $k$ rounds of interaction with the players. Rounds interpolate between the simultaneous and the fully adaptive settings, also capturing parallel complexity. We find that proportional cake cutting in rounds is equivalent to sorting with rank queries in rounds. We design a protocol for proportional cake cutting in rounds, while lower bounds for sorting in rounds with rank queries were given by Alon and Azar. Inspired by the rank query model, we then consider two basic search problems: ordered and unordered search. In unordered search, we get an array $\vec{x}=(x_1, \ldots, x_n)$ and an element $z$ promised to be in $\vec{x}$. We have access to an oracle that receives queries of the form "Is $z$ at location $i$?" and answers "Yes" or "No". The goal is to find the location of $z$ with success probability at least $p$ in at most $k$ rounds of interaction with the oracle. We show the expected query complexity of randomized algorithms on a worst case input is $np\bigl(\frac{k+1}{2k}\bigr) \pm O(1)$, while that of deterministic algorithms on a worst case input distribution is $np \bigl(1 - \frac{k-1}{2k}p \bigr) \pm O(1)$. These bounds apply even to fully adaptive unordered search, where the ratio between the two complexities converges to $2-p$ as the size of the array grows. In ordered search, we get sorted array $\vec{x}=(x_1, \ldots, x_n)$ and element $z$ promised to be in $\vec{x}$. We have access to an oracle that gets comparison queries. Here we find that the expected query complexity of randomized algorithms on a worst case input and deterministic algorithms on a worst case input distribution is essentially the same: $p k \cdot n^{\frac{1}{k}} \pm O(1+pk)$.
Domain Adaptation with Incomplete Target Domains
Venue: arXiv cs.LG 2023
Year: 2023

Domain adaptation, as a task of reducing the annotation cost in a target domain by exploiting the existing labeled data in an auxiliary source domain, has received a lot of attention in the research community. However, the standard domain adaptation has assumed perfectly observed data in both domains, while in real world applications the existence of missing data can be prevalent. In this paper, we tackle a more challenging domain adaptation scenario where one has an incomplete target domain with partially observed data. We propose an Incomplete Data Imputation based Adversarial Network (IDIAN) model to address this new domain adaptation challenge. In the proposed model, we design a data imputation module to fill the missing feature values based on the partial observations in the target domain, while aligning the two domains via deep adversarial adaption. We conduct experiments on both cross-domain benchmark tasks and a real world adaptation task with imperfect target domains. The experimental results demonstrate the effectiveness of the proposed method.
Parallel Residual Bi-Fusion Feature Pyramid Network for Accurate Single-Shot Object Detection
Venue: arXiv cs.CV 2023
Year: 2023

This paper proposes the Parallel Residual Bi-Fusion Feature Pyramid Network (PRB-FPN) for fast and accurate single-shot object detection. Feature Pyramid (FP) is widely used in recent visual detection, however the top-down pathway of FP cannot preserve accurate localization due to pooling shifting. The advantage of FP is weakened as deeper backbones with more layers are used. In addition, it cannot keep up accurate detection of both small and large objects at the same time. To address these issues, we propose a new parallel FP structure with bi-directional (top-down and bottom-up) fusion and associated improvements to retain high-quality features for accurate localization. We provide the following design improvements: (1) A parallel bifusion FP structure with a bottom-up fusion module (BFM) to detect both small and large objects at once with high accuracy. (2) A concatenation and re-organization (CORE) module provides a bottom-up pathway for feature fusion, which leads to the bi-directional fusion FP that can recover lost information from lower-layer feature maps. (3) The CORE feature is further purified to retain richer contextual information. Such CORE purification in both top-down and bottom-up pathways can be finished in only a few iterations. (4) The adding of a residual design to CORE leads to a new Re-CORE module that enables easy training and integration with a wide range of deeper or lighter backbones. The proposed network achieves state-of-the-art performance on the UAVDT17 and MS COCO datasets. Code is available at https://github.com/pingyang1117/PRBNet_PyTorch.
Mapping Patterns for Virtual Knowledge Graphs
Venue: arXiv cs.AI 2023
Year: 2023

Virtual Knowledge Graphs (VKG) constitute one of the most promising paradigms for integrating and accessing legacy data sources. A critical bottleneck in the integration process involves the definition, validation, and maintenance of mappings that link data sources to a domain ontology. To support the management of mappings throughout their entire lifecycle, we propose a comprehensive catalog of sophisticated mapping patterns that emerge when linking databases to ontologies. To do so, we build on well-established methodologies and patterns studied in data management, data analysis, and conceptual modeling. These are extended and refined through the analysis of concrete VKG benchmarks and real-world use cases, and considering the inherent impedance mismatch between data sources and ontologies. We validate our catalog on the considered VKG scenarios, showing that it covers the vast majority of patterns present therein.
Unsupervised embedding of trajectories captures the latent structure of scientific migration
Venue: arXiv cs.LG 2023
Year: 2023

Human migration and mobility drives major societal phenomena including epidemics, economies, innovation, and the diffusion of ideas. Although human mobility and migration have been heavily constrained by geographic distance throughout the history, advances and globalization are making other factors such as language and culture increasingly more important. Advances in neural embedding models, originally designed for natural language, provide an opportunity to tame this complexity and open new avenues for the study of migration. Here, we demonstrate the ability of the model word2vec to encode nuanced relationships between discrete locations from migration trajectories, producing an accurate, dense, continuous, and meaningful vector-space representation. The resulting representation provides a functional distance between locations, as well as a digital double that can be distributed, re-used, and itself interrogated to understand the many dimensions of migration. We show that the unique power of word2vec to encode migration patterns stems from its mathematical equivalence with the gravity model of mobility. Focusing on the case of scientific migration, we apply word2vec to a database of three million migration trajectories of scientists derived from the affiliations listed on their publication records. Using techniques that leverage its semantic structure, we demonstrate that embeddings can learn the rich structure that underpins scientific migration, such as cultural, linguistic, and prestige relationships at multiple levels of granularity. Our results provide a theoretical foundation and methodological framework for using neural embeddings to represent and understand migration both within and beyond science.
Euclidean-Norm-Induced Schatten-p Quasi-Norm Regularization for Low-Rank Tensor Completion and Tensor Robust Principal Component Analysis
Venue: arXiv cs.LG 2023
Year: 2023

The nuclear norm and Schatten-$p$ quasi-norm are popular rank proxies in low-rank matrix recovery. However, computing the nuclear norm or Schatten-$p$ quasi-norm of a tensor is hard in both theory and practice, hindering their application to low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). In this paper, we propose a new class of tensor rank regularizers based on the Euclidean norms of the CP component vectors of a tensor and show that these regularizers are monotonic transformations of tensor Schatten-$p$ quasi-norm. This connection enables us to minimize the Schatten-$p$ quasi-norm in LRTC and TRPCA implicitly via the component vectors. The method scales to big tensors and provides an arbitrarily sharper rank proxy for low-rank tensor recovery compared to the nuclear norm. On the other hand, we study the generalization abilities of LRTC with the Schatten-$p$ quasi-norm regularizer and LRTC with the proposed regularizers. The theorems show that a relatively sharper regularizer leads to a tighter error bound, which is consistent with our numerical results. Particularly, we prove that for LRTC with Schatten-$p$ quasi-norm regularizer on $d$-order tensors, $p=1/d$ is always better than any $p>1/d$ in terms of the generalization ability. We also provide a recovery error bound to verify the usefulness of small $p$ in the Schatten-$p$ quasi-norm for TRPCA. Numerical results on synthetic data and real data demonstrate the effectiveness of the regularization methods and theorems.
Stronger Calibration Lower Bounds via Sidestepping
Venue: arXiv cs.LG 2023
Year: 2023

We consider an online binary prediction setting where a forecaster observes a sequence of $T$ bits one by one. Before each bit is revealed, the forecaster predicts the probability that the bit is $1$. The forecaster is called well-calibrated if for each $p \in [0, 1]$, among the $n_p$ bits for which the forecaster predicts probability $p$, the actual number of ones, $m_p$, is indeed equal to $p \cdot n_p$. The calibration error, defined as $\sum_p |m_p - p n_p|$, quantifies the extent to which the forecaster deviates from being well-calibrated. It has long been known that an $O(T^{2/3})$ calibration error is achievable even when the bits are chosen adversarially, and possibly based on the previous predictions. However, little is known on the lower bound side, except an $Ω(\sqrt{T})$ bound that follows from the trivial example of independent fair coin flips. In this paper, we prove an $Ω(T^{0.528})$ bound on the calibration error, which is the first super-$\sqrt{T}$ lower bound for this setting to the best of our knowledge. The technical contributions of our work include two lower bound techniques, early stopping and sidestepping, which circumvent the obstacles that have previously hindered strong calibration lower bounds. We also propose an abstraction of the prediction setting, termed the Sign-Preservation game, which may be of independent interest. This game has a much smaller state space than the full prediction setting and allows simpler analyses. The $Ω(T^{0.528})$ lower bound follows from a general reduction theorem that translates lower bounds on the game value of Sign-Preservation into lower bounds on the calibration error.
Your College Dorm and Dormmates: Fair Resource Sharing with Externalities
Venue: arXiv cs.GT 2023
Year: 2023

We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, who share the same resource with them. Clearly, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even deciding the existence of such a strongly envy-free assignment is an intractable problem. Hence, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved. Under this relaxed notion, an agent envies another only when they envy both the resource and the mates of the other agent. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dormmates. We show that when the capacity of each dorm is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment. Nevertheless, the result breaks immediately when the capacity increases to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the utility guarantees of (Pareto) envy-free assignments in our model.
Minimax Regret Optimisation for Robust Planning in Uncertain Markov Decision Processes
Venue: arXiv cs.AI 2023
Year: 2023

The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for planning in UMDPs to find robust policies which are not overly conservative. In this work, we focus on planning for Stochastic Shortest Path (SSP) UMDPs with uncertain cost and transition functions. We introduce a Bellman equation to compute the regret for a policy. We propose a dynamic programming algorithm that utilises the regret Bellman equation, and show that it optimises minimax regret exactly for UMDPs with independent uncertainties. For coupled uncertainties, we extend our approach to use options to enable a trade off between computation and solution quality. We evaluate our approach on both synthetic and real-world domains, showing that it significantly outperforms existing baselines.
INSPIRE: Intensity and spatial information-based deformable image registration
Venue: arXiv cs.CV 2023
Year: 2023

We present INSPIRE, a top-performing general-purpose method for deformable image registration. INSPIRE brings distance measures which combine intensity and spatial information into an elastic B-splines-based transformation model and incorporates an inverse inconsistency penalization supporting symmetric registration performance. We introduce several theoretical and algorithmic solutions which provide high computational efficiency and thereby applicability of the proposed framework in a wide range of real scenarios. We show that INSPIRE delivers highly accurate, as well as stable and robust registration results. We evaluate the method on a 2D dataset created from retinal images, characterized by presence of networks of thin structures. Here INSPIRE exhibits excellent performance, substantially outperforming the widely used reference methods. {We also evaluate INSPIRE on the Fundus Image Registration Dataset (FIRE), which consists of 134 pairs of separately acquired retinal images. INSPIRE exhibits excellent performance on the FIRE dataset, substantially outperforming several domain-specific methods.} We also evaluate the method on four benchmark datasets of 3D magnetic resonance images of brains, for a total of 2088 pairwise registrations. A comparison with 17 other state-of-the-art methods reveals that INSPIRE provides the best overall performance. Code is available at http://github.com/MIDA-group/inspire
Continuous Positional Payoffs
Venue: arXiv cs.GT 2023
Year: 2023

What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined payoffs are interesting is that they include the multi-discounted payoffs. We show that for continuous payoffs, positional determinacy is equivalent to a simple property called prefix-monotonicity. We provide three proofs of it, using three major techniques of establishing positional determinacy -- inductive technique, fixed point technique and strategy improvement technique. A combination of these approaches provides us with better understanding of the structure of continuous positionally determined payoffs as well as with some algorithmic results.