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Yining Wang

Publications and source records attributed to Yining Wang.

At least 109 records · Page 6Linked to original sources
arXiv2019

An Optimal Policy for Dynamic Assortment Planning Under Uncapacitated Multinomial Logit Models

We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Since all the utility parameters of MNL are unknown, the seller needs to simultaneously learn customers' choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products $N$. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model---MNL model is still open. By carefully analyzing a revenue potential function, we develop a trisection based policy combined with adaptive confidence bound construction, which achieves an {item-independent} regret bound of $O(\sqrt{T})$, where $T$ is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There are two major advantages of the proposed policy. First, the regret of all our policies has no dependence on $N$. Second, our policies are almost assumption free: there is no assumption on mean utility nor any "separability" condition on the expected revenues for different assortments. Our result also extends the unimodal bandit literature.

stat.ML↗
arXiv2019

Dynamic Assortment Optimization with Changing Contextual Information

In this paper, we study the dynamic assortment optimization problem under a finite selling season of length $T$. At each time period, the seller offers an arriving customer an assortment of substitutable products under a cardinality constraint, and the customer makes the purchase among offered products according to a discrete choice model. Most existing work associates each product with a real-valued fixed mean utility and assumes a multinomial logit choice (MNL) model. In many practical applications, feature/contexutal information of products is readily available. In this paper, we incorporate the feature information by assuming a linear relationship between the mean utility and the feature. In addition, we allow the feature information of products to change over time so that the underlying choice model can also be non-stationary. To solve the dynamic assortment optimization under this changing contextual MNL model, we need to simultaneously learn the underlying unknown coefficient and makes the decision on the assortment. To this end, we develop an upper confidence bound (UCB) based policy and establish the regret bound on the order of $\widetilde O(d\sqrt{T})$, where $d$ is the dimension of the feature and $\widetilde O$ suppresses logarithmic dependence. We further established the lower bound $Ω(d\sqrt{T}/K)$ where $K$ is the cardinality constraint of an offered assortment, which is usually small. When $K$ is a constant, our policy is optimal up to logarithmic factors. In the exploitation phase of the UCB algorithm, we need to solve a combinatorial optimization for assortment optimization based on the learned information. We further develop an approximation algorithm and an efficient greedy heuristic. The effectiveness of the proposed policy is further demonstrated by our numerical studies.

econ.EM↗
arXiv2018

Efficient Load Sampling for Worst-Case Structural Analysis Under Force Location Uncertainty

An important task in structural design is to quantify the structural performance of an object under the external forces it may experience during its use. The problem proves to be computationally very challenging as the external forces' contact locations and magnitudes may exhibit significant variations. We present an efficient analysis approach to determine the most critical force contact location in such problems with force location uncertainty. Given an input 3D model and regions on its boundary where arbitrary normal forces may make contact, our algorithm predicts the worst-case force configuration responsible for creating the highest stress within the object. Our approach uses a computationally tractable experimental design method to select number of sample force locations based on geometry only, without inspecting the stress response that requires computationally expensive finite-element analysis. Then, we construct a simple regression model on these samples and corresponding maximum stresses. Combined with a simple ranking based post-processing step, our method provides a practical solution to worst-case structural analysis problem. The results indicate that our approach achieves significant improvements over the existing work and brute force approaches. We demonstrate that further speed- up can be obtained when small amount of an error tolerance in maximum stress is allowed.

stat.ML↗
arXiv2018

A Note on a Tight Lower Bound for MNL-Bandit Assortment Selection Models

In this short note we consider a dynamic assortment planning problem under the capacitated multinomial logit (MNL) bandit model. We prove a tight lower bound on the accumulated regret that matches existing regret upper bounds for all parameters (time horizon $T$, number of items $N$ and maximum assortment capacity $K$) up to logarithmic factors. Our results close an $O(\sqrt{K})$ gap between upper and lower regret bounds from existing works.

stat.ML↗
arXiv2018

Sequence Modeling via Segmentations

Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is calculated as the product of the probabilities of all its segments, where each segment is modeled using existing tools such as recurrent neural networks. Since the segmentation of a sequence is usually unknown in advance, we sum over all valid segmentations to obtain the final probability for the sequence. An efficient dynamic programming algorithm is developed for forward and backward computations without resorting to any approximation. We demonstrate our approach on text segmentation and speech recognition tasks. In addition to quantitative results, we also show that our approach can discover meaningful segments in their respective application contexts.

stat.ML↗
arXiv2018

Fe3O4@astragalus polysaccharide core-shell nanoparticles for iron deficiency anemia therapy and magnetic resonance imaging in vivo

Fe3O4@astragalus polysaccharide core-shell nanoparticles (Fe3O4@APS NPs) were demonstrated to be an efficient therapeutic drug for treating iron deficiency anemia (IDA) in vivo. The Fe3O4@APS NPs have been synthesized using a two steps approach involving hydrothermal synthesis and subsequent esterification. Transmission electron microscopy (TEM) and Fourier transform infrared (FTIR) spectroscopy studies show that APS are attached on the surfaces of the highly monodisperse Fe3O4 NPs. Dynamic light scatting (DLS) and magnetic characterizations reveal that the Fe3O4@APS NPs have outstanding water solubility and stability. Cytotoxicity assessment using Hela cells and pathological tests in mice demonstrate their good biocompatibility and low toxicity. The IDA treatment in rats shows that they have efficient therapeutic effect, which is contributed to both the iron element supplement from Fe3O4 and the APS-stimulated hematopoietic cell generation. Moreover, the Fe3O4@APS NPs are superparamagnetic and thus able to be used for magnetic resonance imaging (MRI). This study has demonstrated the potential of nanocomposites involving purified natural products from Chinese herb medicine for biomedical applications.

physics.bio-ph↗
arXiv2018

Robust Nonparametric Regression under Huber's $ε$-contamination Model

We consider the non-parametric regression problem under Huber's $ε$-contamination model, in which an $ε$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up to absolute constants over the Hölder function class with smoothness parameters smaller than or equal to 1. Furthermore, when the underlying function has higher smoothness, we show that using local binning median as pre-preprocessing step to remove the adversarial noise, then we can apply any non-parametric estimator on top of the medians. In particular we show local median binning followed by kernel smoothing and local polynomial regression achieve minimaxity over Hölder and Sobolev classes with arbitrary smoothness parameters. Our main proof technique is a decoupled analysis of adversary noise and stochastic noise, which can be potentially applied to other robust estimation problems. We also provide numerical results to verify the effectiveness of our proposed methods.

math.ST↗
arXiv2018

Phrase Table as Recommendation Memory for Neural Machine Translation

Neural Machine Translation (NMT) has drawn much attention due to its promising translation performance recently. However, several studies indicate that NMT often generates fluent but unfaithful translations. In this paper, we propose a method to alleviate this problem by using a phrase table as recommendation memory. The main idea is to add bonus to words worthy of recommendation, so that NMT can make correct predictions. Specifically, we first derive a prefix tree to accommodate all the candidate target phrases by searching the phrase translation table according to the source sentence. Then, we construct a recommendation word set by matching between candidate target phrases and previously translated target words by NMT. After that, we determine the specific bonus value for each recommendable word by using the attention vector and phrase translation probability. Finally, we integrate this bonus value into NMT to improve the translation results. The extensive experiments demonstrate that the proposed methods obtain remarkable improvements over the strong attentionbased NMT.

cs.CL↗
arXiv2018

Non-stationary Stochastic Optimization under $L_{p,q}$-Variation Measures

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which yields less variation for dynamic function sequences whose changes are constrained to short time periods or small subsets of input domain. Under the $L_{p,q}$-variation constraint, we derive both upper and matching lower regret bounds for smooth and strongly convex function sequences, which generalize previous results in Besbes et al. (2015). Furthermore, we provide an upper bound for general convex function sequences with noisy gradient feedback, which matches the optimal rate as $p\to\infty$. Our results reveal some surprising phenomena under this general variation functional, such as the curse of dimensionality of the function domain. The key technical novelties in our analysis include affinity lemmas that characterize the distance of the minimizers of two convex functions with bounded Lp difference, and a cubic spline based construction that attains matching lower bounds.

stat.ML↗
arXiv2018

Optimization of Smooth Functions with Noisy Observations: Local Minimax Rates

We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy evaluations of function values at the queried points (i.e. the algorithm has access to zeroth-order information). Optimization performance is evaluated by the expected difference of function values at the estimated optimum and the true optimum. In contrast to the classical optimization setup, first-order information like gradients are not directly accessible to the optimization algorithm. We show that the classical minimax framework of analysis, which roughly characterizes the worst-case query complexity of an optimization algorithm in this setting, leads to excessively pessimistic results. We propose a local minimax framework to study the fundamental difficulty of optimizing smooth functions with adaptive function evaluations, which provides a refined picture of the intrinsic difficulty of zeroth-order optimization. We show that for functions with fast level set growth around the global minimum, carefully designed optimization algorithms can identify a near global minimizer with many fewer queries. For the special case of strongly convex and smooth functions, our implied convergence rates match the ones developed for zeroth-order convex optimization problems. At the other end of the spectrum, for worst-case smooth functions no algorithm can converge faster than the minimax rate of estimating the entire unknown function in the $\ell_\infty$-norm. We provide an intuitive and efficient algorithm that attains the derived upper error bounds.

stat.ML↗
arXiv2018

Convergence Rates of Latent Topic Models Under Relaxed Identifiability Conditions

In this paper we study the frequentist convergence rate for the Latent Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum likelihood estimator converges to one of the finitely many equivalent parameters in Wasserstein's distance metric at a rate of $n^{-1/4}$ without assuming separability or non-degeneracy of the underlying topics and/or the existence of more than three words per document, thus generalizing the previous works of Anandkumar et al. (2012, 2014) from an information-theoretical perspective. We also show that the $n^{-1/4}$ convergence rate is optimal in the worst case.

stat.ML↗
arXiv2018

Stochastic Zeroth-order Optimization in High Dimensions

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that de- pend only logarithmically on the ambient dimension of the problem. Empirical results confirm our theoretical findings and show that the algorithms we design outperform classical zeroth-order optimization methods in the high-dimensional setting.

stat.ML↗
arXiv2018

Direct Learning to Rank and Rerank

Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a serious problem with the state of learning-to-rank algorithms, which is that they are based on convex proxies that lead to poor approximations. We then discuss the possibility of "exact" reranking algorithms based on mathematical programming. We prove that a relaxed version of the "exact" problem has the same optimal solution, and provide an empirical analysis.

stat.ML↗
arXiv2018

Provably Correct Algorithms for Matrix Column Subset Selection with Selectively Sampled Data

We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to numerous real-world data applications such as population genetics summarization, electronic circuits testing and recommendation systems. In many applications the complete data matrix is unavailable and one needs to select representative columns by inspecting only a small portion of the input matrix. In this paper we propose the first provably correct column subset selection algorithms for partially observed data matrices. Our proposed algorithms exhibit different merits and limitations in terms of statistical accuracy, computational efficiency, sample complexity and sampling schemes, which provides a nice exploration of the tradeoff between these desired properties for column subset selection. The proposed methods employ the idea of feedback driven sampling and are inspired by several sampling schemes previously introduced for low-rank matrix approximation tasks (Drineas et al., 2008; Frieze et al., 2004; Deshpande and Vempala, 2006; Krishnamurthy and Singh, 2014). Our analysis shows that, under the assumption that the input data matrix has incoherent rows but possibly coherent columns, all algorithms provably converge to the best low-rank approximation of the original data as number of selected columns increases. Furthermore, two of the proposed algorithms enjoy a relative error bound, which is preferred for column subset selection and matrix approximation purposes. We also demonstrate through both theoretical and empirical analysis the power of feedback driven sampling compared to uniform random sampling on input matrices with highly correlated columns.

stat.ML↗
arXiv2017

On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models

We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models and Delta's method (estimating functions of linear regression models) as well. The algorithms are based on a continuous relaxation of an otherwise intractable combinatorial optimization problem, with sampling or greedy procedures as post-processing steps. Formal approximation guarantees are established for both algorithms, and numerical results on both synthetic and real-world data confirm the effectiveness of the proposed methods.

stat.ML↗
arXiv2017

Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency is measured by optimality criteria, including A(verage), D(eterminant), T(race), E(igen), V(ariance) and G-optimality. Except for the T-optimality, exact optimization is NP-hard. We propose a polynomial-time regret minimization framework to achieve a $(1+\varepsilon)$ approximation with only $O(p/\varepsilon^2)$ design points, for all the optimality criteria above. In contrast, to the best of our knowledge, before our work, no polynomial-time algorithm achieves $(1+\varepsilon)$ approximations for D/E/G-optimality, and the best poly-time algorithm achieving $(1+\varepsilon)$-approximation for A/V-optimality requires $k = Ω(p^2/\varepsilon)$ design points.

stat.ML↗
arXiv2017

Word, Subword or Character? An Empirical Study of Granularity in Chinese-English NMT

Neural machine translation (NMT), a new approach to machine translation, has been proved to outperform conventional statistical machine translation (SMT) across a variety of language pairs. Translation is an open-vocabulary problem, but most existing NMT systems operate with a fixed vocabulary, which causes the incapability of translating rare words. This problem can be alleviated by using different translation granularities, such as character, subword and hybrid word-character. Translation involving Chinese is one of the most difficult tasks in machine translation, however, to the best of our knowledge, there has not been any other work exploring which translation granularity is most suitable for Chinese in NMT. In this paper, we conduct an extensive comparison using Chinese-English NMT as a case study. Furthermore, we discuss the advantages and disadvantages of various translation granularities in detail. Our experiments show that subword model performs best for Chinese-to-English translation with the vocabulary which is not so big while hybrid word-character model is most suitable for English-to-Chinese translation. Moreover, experiments of different granularities show that Hybrid_BPE method can achieve best result on Chinese-to-English translation task.

cs.CL↗