To address the challenge of choice congestion in matching markets, in this work, we introduce a two-sided assortment optimization framework under general choice preferences. The goal in this problem is to maximize the expected number of matches by deciding which assortments are displayed to the agents and the order in which they are shown. In this context, we identify several classes of policies that platforms can use in their design. Our goals are: (1) to measure the value that one class of policies has over another one, and (2) to approximately solve the optimization problem itself for a given class. For (1), we define the adaptivity gap as the worst-case ratio between the optimal values of two different policy classes. First, we show that the gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly $1-1/e$. Second, we show that the gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly $1/2$. We also note that the worst policies are those who simultaneously show assortments to all the agents, in fact, we show that their adaptivity gap even with respect to one-sided static policies can be arbitrarily small. For (2), we first show that there exists a polynomial time policy that achieves a $1/4$ approximation factor within the class of policies that adaptively show assortments to agents one by one. Finally, when agents' preferences are governed by multinomial-logit models, we show that a 0.066 approximation factor can be obtained within the class of policies that show assortments to all agents at once.
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Real world testing is of vital importance to the success of automated driving. While many players in the business design purpose build testing vehicles, we designed and build a modular platform that offers high flexibility for any kind of scenario. CoCar NextGen is equipped with next generation hardware that addresses all future use cases. Its extensive, redundant sensor setup allows to develop cross-domain data driven approaches that manage the transfer to other sensor setups. Together with the possibility of being deployed on public roads, this creates a unique research platform that supports the road to automated driving on SAE Level 5.
In this work, we consider pattern matching variants in small space, that is, in the read-only setting, where we want to bound the space usage on top of storing the strings. Our main contribution is a space-time trade-off for the Internal Pattern Matching (IPM) problem, where the goal is to construct a data structure over a string $S$ of length $n$ that allows one to answer the following type of queries: Compute the occurrences of a fragment $P$ of $S$ inside another fragment $T$ of $S$, provided that $|T| < 2|P|$. For any $\tau \in [1 .. n/\log^2 n]$, we present a nearly-optimal $\~O(n/\tau)$-size data structure that can be built in $\~O(n)$ time using $\~O(n/\tau)$ extra space, and answers IPM queries in $O(\tau+\log n \log^3 \log n)$ time. IPM queries have been identified as a crucial primitive operation for the analysis of algorithms on strings. In particular, the complexities of several recent algorithms for approximate pattern matching are expressed with regards to the number of calls to a small set of primitive operations that include IPM queries; our data structure allows us to port these results to the small-space setting. We further showcase the applicability of our IPM data structure by using it to obtain space-time trade-offs for the longest common substring and circular pattern matching problems in the asymmetric streaming setting.
The Plurality rule for linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the alternatives least often occurring in the final position. We explore extensions of these rules to partial orders, offering axiomatic characterizations for these extensions.
In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite its simplicity, differentially private continual counting has attracted significant attention both in theory and in practice. Existing algorithms for differentially private continual counting are either inefficient in terms of their space usage or add an excessive amount of noise, inducing suboptimal utility. The most practical DP continual counting algorithms add carefully correlated Gaussian noise to the values. The task of choosing the covariance for this noise can be expressed in terms of factoring the lower-triangular matrix of ones (which computes prefix sums). We present two approaches from this class (for different parameter regimes) that achieve near-optimal utility for DP continual counting and only require logarithmic or polylogarithmic space (and time). Our first approach is based on a space-efficient streaming matrix multiplication algorithm for a class of Toeplitz matrices. We show that to instantiate this algorithm for DP continual counting, it is sufficient to find a low-degree rational function that approximates the square root on a circle in the complex plane. We then apply and extend tools from approximation theory to achieve this. We also derive efficient closed-forms for the objective function for arbitrarily many steps, and show direct numerical optimization yields a highly practical solution to the problem. Our second approach combines our first approach with a recursive construction similar to the binary tree mechanism.
Current recommendation systems are significantly affected by a serious issue of temporal data shift, which is the inconsistency between the distribution of historical data and that of online data. Most existing models focus on utilizing updated data, overlooking the transferable, temporal data shift-free information that can be learned from shifting data. We propose the Temporal Invariance of Association theorem, which suggests that given a fixed search space, the relationship between the data and the data in the search space keeps invariant over time. Leveraging this principle, we designed a retrieval-based recommendation system framework that can train a data shift-free relevance network using shifting data, significantly enhancing the predictive performance of the original model in the recommendation system. However, retrieval-based recommendation models face substantial inference time costs when deployed online. To address this, we further designed a distill framework that can distill information from the relevance network into a parameterized module using shifting data. The distilled model can be deployed online alongside the original model, with only a minimal increase in inference time. Extensive experiments on multiple real datasets demonstrate that our framework significantly improves the performance of the original model by utilizing shifting data.
PageRank is a widely used centrality measure that "ranks" vertices in a graph by considering the connections and their importance. In this report, we first introduce one of the most efficient GPU implementations of Static PageRank, which recomputes PageRank scores from scratch. It uses a synchronous pull-based atomics-free PageRank computation, with the low and high in-degree vertices being partitioned and processed by two separate kernels. Next, we present our GPU implementation of incrementally expanding (and contracting) Dynamic Frontier with Pruning (DF-P) PageRank, which processes only a subset of vertices likely to change ranks. It is based on Static PageRank, and uses an additional partitioning between low and high out-degree vertices for incremental expansion of the set of affected vertices with two additional kernels. On a server with an NVIDIA A100 GPU, our Static PageRank outperforms Hornet and Gunrock's PageRank implementations by 31x and 5.9x respectively. On top of the above, DF-P PageRank outperforms Static PageRank by 2.1x on real-world dynamic graphs, and by 3.1x on large static graphs with random batch updates.
Images can convey rich semantics and induce various emotions in viewers. Recently, with the rapid advancement of emotional intelligence and the explosive growth of visual data, extensive research efforts have been dedicated to affective image content analysis (AICA). In this survey, we will comprehensively review the development of AICA in the recent two decades, especially focusing on the state-of-the-art methods with respect to three main challenges -- the affective gap, perception subjectivity, and label noise and absence. We begin with an introduction to the key emotion representation models that have been widely employed in AICA and description of available datasets for performing evaluation with quantitative comparison of label noise and dataset bias. We then summarize and compare the representative approaches on (1) emotion feature extraction, including both handcrafted and deep features, (2) learning methods on dominant emotion recognition, personalized emotion prediction, emotion distribution learning, and learning from noisy data or few labels, and (3) AICA based applications. Finally, we discuss some challenges and promising research directions in the future, such as image content and context understanding, group emotion clustering, and viewer-image interaction.
Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.
Object detectors usually achieve promising results with the supervision of complete instance annotations. However, their performance is far from satisfactory with sparse instance annotations. Most existing methods for sparsely annotated object detection either re-weight the loss of hard negative samples or convert the unlabeled instances into ignored regions to reduce the interference of false negatives. We argue that these strategies are insufficient since they can at most alleviate the negative effect caused by missing annotations. In this paper, we propose a simple but effective mechanism, called Co-mining, for sparsely annotated object detection. In our Co-mining, two branches of a Siamese network predict the pseudo-label sets for each other. To enhance multi-view learning and better mine unlabeled instances, the original image and corresponding augmented image are used as the inputs of two branches of the Siamese network, respectively. Co-mining can serve as a general training mechanism applied to most of modern object detectors. Experiments are performed on MS COCO dataset with three different sparsely annotated settings using two typical frameworks: anchor-based detector RetinaNet and anchor-free detector FCOS. Experimental results show that our Co-mining with RetinaNet achieves 1.4%~2.1% improvements compared with different baselines and surpasses existing methods under the same sparsely annotated setting.
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.
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