Fusing regression coefficients into homogenous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called $L_0$-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called grouping sensitivity that underpins the difficulty of recovering the true groups. We show that $L_0$-Fusion achieves grouping consistency under the weakest possible requirement of the grouping sensitivity: if this requirement is violated, then the minimax risk of group misspecification will fail to converge to zero. Moreover, we show that in the high-dimensional regime, one can apply $L_0$-Fusion coupled with a sure screening set of features without any essential loss of statistical efficiency, while reducing the computational cost substantially. On the algorithmic aspect, we provide a MIO formulation for $L_0$-Fusion along with a warm start strategy. Simulation and real data analysis demonstrate that $L_0$-Fusion exhibits superiority over its competitors in terms of grouping accuracy.
相關內容
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated by the growing number of new iterations proposed for increasingly complex problems, ranging from multi-layer inference to low-rank matrix estimation with elaborate priors. In this paper, we address the following questions: is there a structure underlying all AMP iterations that unifies them in a common framework? Can we use such a structure to give a modular proof of state evolution equations, adaptable to new AMP iterations without reproducing each time the full argument ? We propose an answer to both questions, showing that AMP instances can be generically indexed by an oriented graph. This enables to give a unified interpretation of these iterations, independent from the problem they solve, and a way of composing them arbitrarily. We then show that all AMP iterations indexed by such a graph admit rigorous SE equations, extending the reach of previous proofs, and proving a number of recent heuristic derivations of those equations. Our proof naturally includes non-separable functions and we show how existing refinements, such as spatial coupling or matrix-valued variables, can be combined with our framework.
We consider the question of adaptive data analysis within the framework of convex optimization. We ask how many samples are needed in order to compute $\epsilon$-accurate estimates of $O(1/\epsilon^2)$ gradients queried by gradient descent, and we provide two intermediate answers to this question. First, we show that for a general analyst (not necessarily gradient descent) $\Omega(1/\epsilon^3)$ samples are required. This rules out the possibility of a foolproof mechanism. Our construction builds upon a new lower bound (that may be of interest of its own right) for an analyst that may ask several non adaptive questions in a batch of fixed and known $T$ rounds of adaptivity and requires a fraction of true discoveries. We show that for such an analyst $\Omega (\sqrt{T}/\epsilon^2)$ samples are necessary. Second, we show that, under certain assumptions on the oracle, in an interaction with gradient descent $\tilde \Omega(1/\epsilon^{2.5})$ samples are necessary. Our assumptions are that the oracle has only \emph{first order access} and is \emph{post-hoc generalizing}. First order access means that it can only compute the gradients of the sampled function at points queried by the algorithm. Our assumption of \emph{post-hoc generalization} follows from existing lower bounds for statistical queries. More generally then, we provide a generic reduction from the standard setting of statistical queries to the problem of estimating gradients queried by gradient descent. These results are in contrast with classical bounds that show that with $O(1/\epsilon^2)$ samples one can optimize the population risk to accuracy of $O(\epsilon)$ but, as it turns out, with spurious gradients.
On-demand delivery has become increasingly popular around the world. Motivated by a large grocery chain store who offers fast on-demand delivery services, we model and solve a stochastic dynamic driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The system operator needs to dispatch a set of drivers and specify their delivery routes facing random demand that arrives over a fixed number of periods. The resulting stochastic dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel structured approximation framework to approximate the value function via a parametrized dispatching and routing policy. We analyze the structural properties of the approximation framework and establish its performance guarantee under large-demand scenarios. We then develop efficient exact algorithms for the approximation problem based on Benders decomposition and column generation, which deliver verifiably optimal solutions within minutes. The evaluation results on a real-world data set show that our framework outperforms the current policy of the company by 36.53% on average in terms of delivery time. We also perform several policy experiments to understand the value of dynamic dispatching and routing with varying fleet sizes and dispatch frequencies.
Binary pointwise labels (aka implicit feedback) are heavily leveraged by deep learning based recommendation algorithms nowadays. In this paper we discuss the limited expressiveness of these labels may fail to accommodate varying degrees of user preference, and thus lead to conflicts during model training, which we call annotation bias. To solve this issue, we find the soft-labeling property of pairwise labels could be utilized to alleviate the bias of pointwise labels. To this end, we propose a momentum contrast framework (MP2) that combines pointwise and pairwise learning for recommendation. MP2 has a three-tower network structure: one user network and two item networks. The two item networks are used for computing pointwise and pairwise loss respectively. To alleviate the influence of the annotation bias, we perform a momentum update to ensure a consistent item representation. Extensive experiments on real-world datasets demonstrate the superiority of our method against state-of-the-art recommendation algorithms.
The security of quantum key distribution (QKD) is severely threatened by discrepancies between realistic devices and theoretical assumptions. Recently, a significant framework called the reference technique was proposed to provide security against arbitrary source flaws, including pulse correlations. Here, we propose an efficient four-phase twin-field QKD using laser pulses adopting the reference technique for security against all possible source imperfections. We present a characterization of source flaws and connect them to experimental data, together with a finite-key analysis. In addition, we demonstrate the feasibility of our protocol through a proof-of-principle experimental implementation and demonstrate a secure key rate of 1.63 kbps with a 20 dB channel loss. Compared with previous QKD protocols with imperfect devices, our work considerably improves both the secure key rate and the transmission distance, and shows application potential in the practical deployment of secure QKD with device imperfections.
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of maintaining a MaxIS over dynamic graphs has attracted increasing attention over the past few years. Due to the intractability of maintaining an exact MaxIS, this paper aims to develop efficient algorithms that can maintain an approximate MaxIS with an accuracy guarantee theoretically. In particular, we propose a framework that maintains a $(\frac{\Delta}{2} + 1)$-approximate MaxIS over dynamic graphs and prove that it achieves a constant approximation ratio in many real-world networks. To the best of our knowledge, this is the first non-trivial approximability result for the dynamic MaxIS problem. Following the framework, we implement an efficient linear-time dynamic algorithm and a more effective dynamic algorithm with near-linear expected time complexity. Our thorough experiments over real and synthetic graphs demonstrate the effectiveness and efficiency of the proposed algorithms, especially when the graph is highly dynamic.
Video search has become the main routine for users to discover videos relevant to a text query on large short-video sharing platforms. During training a query-video bi-encoder model using online search logs, we identify a modality bias phenomenon that the video encoder almost entirely relies on text matching, neglecting other modalities of the videos such as vision, audio. This modality imbalanceresults from a) modality gap: the relevance between a query and a video text is much easier to learn as the query is also a piece of text, with the same modality as the video text; b) data bias: most training samples can be solved solely by text matching. Here we share our practices to improve the first retrieval stage including our solution for the modality imbalance issue. We propose MBVR (short for Modality Balanced Video Retrieval) with two key components: manually generated modality-shuffled (MS) samples and a dynamic margin (DM) based on visual relevance. They can encourage the video encoder to pay balanced attentions to each modality. Through extensive experiments on a real world dataset, we show empirically that our method is both effective and efficient in solving modality bias problem. We have also deployed our MBVR in a large video platform and observed statistically significant boost over a highly optimized baseline in an A/B test and manual GSB evaluations.
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper, we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We propose combining subsplit Bayesian networks, an expressive graphical model for tree topology distributions, and a structured amortization of the branch lengths over tree topologies for a suitable variational family of distributions. We train the variational approximation via stochastic gradient ascent and adopt gradient estimators for continuous and discrete variational parameters separately to deal with the composite latent space of phylogenetic models. We show that our variational approach provides competitive performance to MCMC, while requiring much less computation due to a more efficient exploration mechanism enabled by variational inference. Experiments on a benchmark of challenging real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods.
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that, grounded on combinatorial considerations, contributes to give new interesting insights both for modelling and theoretical purposes. To this aim, we incorporate the ordinal pattern analysis approach which allows us to abstract a time series as a sequence of patterns and their associated permutations, and introduce a simple functional over permutations that partitions them into classes encoding their level of asymmetry. We compute the exact probability mass function (p.m.f.) of this functional over the symmetric group of degree $n$, thus providing the description for the case of an infinite white noise realization. This p.m.f. can be conveniently approximated by a continuous probability density from an exponential family, the Gaussian, hence providing natural sufficient statistics that render a convenient and simple statistical analysis through ordinal patterns. Such analysis is exemplified on experimental data for the spatial increments from tracks of gold nanoparticles in 3D diffusion.
Stickers with vivid and engaging expressions are becoming increasingly popular in online messaging apps, and some works are dedicated to automatically select sticker response by matching text labels of stickers with previous utterances. However, due to their large quantities, it is impractical to require text labels for the all stickers. Hence, in this paper, we propose to recommend an appropriate sticker to user based on multi-turn dialog context history without any external labels. Two main challenges are confronted in this task. One is to learn semantic meaning of stickers without corresponding text labels. Another challenge is to jointly model the candidate sticker with the multi-turn dialog context. To tackle these challenges, we propose a sticker response selector (SRS) model. Specifically, SRS first employs a convolutional based sticker image encoder and a self-attention based multi-turn dialog encoder to obtain the representation of stickers and utterances. Next, deep interaction network is proposed to conduct deep matching between the sticker with each utterance in the dialog history. SRS then learns the short-term and long-term dependency between all interaction results by a fusion network to output the the final matching score. To evaluate our proposed method, we collect a large-scale real-world dialog dataset with stickers from one of the most popular online chatting platform. Extensive experiments conducted on this dataset show that our model achieves the state-of-the-art performance for all commonly-used metrics. Experiments also verify the effectiveness of each component of SRS. To facilitate further research in sticker selection field, we release this dataset of 340K multi-turn dialog and sticker pairs.
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