This paper studies sequential search models that (1) incorporate unobserved product quality, which can be correlated with endogenous observable characteristics (such as price) and endogenous search cost variables (such as product rankings in online search intermediaries); and (2) do not require researchers to know the true distribution of the match value between consumers and products. A likelihood approach to estimate such models gives biased results. Therefore, I propose a new estimator -- pairwise maximum rank (PMR) estimator -- for both preference and search cost parameters. I show that the PMR estimator is consistent using only data on consumers' search order among one pair of products rather than data on consumers' full consideration set or final purchase. Additionally, we can use the PMR estimator to test for the true match value distribution in the data. In the empirical application, I apply the PMR estimator to quantify the effect of rankings in Expedia hotel search using two samples of the data set, to which consumers are randomly assigned. I find the position effect to be \$0.11-\$0.36, and the effect estimated using the sample with randomly generated rankings is close to the effect estimated using the sample with endogenous rankings. Moreover, I find that the true match value distribution in the data is unlikely to be N(0,1). Likelihood estimation ignoring endogeneity gives an upward bias of at least \$1.17; misspecification of match value distribution as N(0,1) gives an upward bias of at least \$2.99.
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The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of $n$ unobserved i.i.d. terms, the basic classical result is that the relative error in the density is of order $1/n$. If instead the approximation is interpreted as a likelihood and maximised as a function of model parameters, the result is an approximation to the maximum likelihood estimate (MLE) that can be much faster to compute than the true MLE. This paper proves the analogous basic result for the approximation error between the saddlepoint MLE and the true MLE: subject to certain explicit identifiability conditions, the error has asymptotic size $O(1/n^2)$ for some parameters, and $O(1/n^{3/2})$ or $O(1/n)$ for others. In all three cases, the approximation errors are asymptotically negligible compared to the inferential uncertainty. The proof is based on a factorisation of the saddlepoint likelihood into an exact and approximate term, along with an analysis of the approximation error in the gradient of the log-likelihood. This factorisation also gives insight into alternatives to the saddlepoint approximation, including a new and simpler saddlepoint approximation, for which we derive analogous error bounds. As a corollary of our results, we also obtain the asymptotic size of the MLE error approximation when the saddlepoint approximation is replaced by the normal approximation.
We focus on Maximum Inner Product Search (MIPS), which is an essential problem in many machine learning communities. Given a query, MIPS finds the most similar items with the maximum inner products. Methods for Nearest Neighbor Search (NNS) which is usually defined on metric space don't exhibit the satisfactory performance for MIPS problem since inner product is a non-metric function. However, inner products exhibit many good properties compared with metric functions, such as avoiding vanishing and exploding gradients. As a result, inner product is widely used in many recommendation systems, which makes efficient Maximum Inner Product Search a key for speeding up many recommendation systems. Graph based methods for NNS problem show the superiorities compared with other class methods. Each data point of the database is mapped to a node of the proximity graph. Nearest neighbor search in the database can be converted to route on the proximity graph to find the nearest neighbor for the query. This technique can be used to solve MIPS problem. Instead of searching the nearest neighbor for the query, we search the item with maximum inner product with query on the proximity graph. In this paper, we propose a reinforcement model to train an agent to search on the proximity graph automatically for MIPS problem if we lack the ground truths of training queries. If we know the ground truths of some training queries, our model can also utilize these ground truths by imitation learning to improve the agent's search ability. By experiments, we can see that our proposed mode which combines reinforcement learning with imitation learning shows the superiorities over the state-of-the-art methods
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as a new method for estimating the latter's sparse precision (i.e., inverse covariance) matrices. When the sparsity pattern of each matrix is known, we propose an efficient optimization method for the Maximum Likelihood Estimate (MLE) of that matrix. When it is unknown, we utilize the popular Graphical Least Absolute Shrinkage and Selection Operator (GLASSO) to estimate that pattern. However, we show that even for a single Gaussian, when GLASSO is tuned to successfully estimate the sparsity pattern, it does so at the price of a substantial bias of the values of the nonzero entries of the matrix, and we show that this problem only worsens in a mixture setting. To overcome this, we discard the nonzero values estimated by GLASSO, keep only its pattern estimate and use it within the proposed MLE method. This yields an effective two-step procedure that removes the bias. We show that our "debiasing" approach outperforms GLASSO in both the single-GMRF and the GMRF-MM cases. We also show that when learning priors for image patches, our method outperforms GLASSO even if we merely use an educated guess about the sparsity pattern, and that our GMRF-MM outperforms the baseline GMM on real and synthetic high-dimensional datasets.
The advent of transformer-based models such as BERT has led to the rise of neural ranking models. These models have improved the effectiveness of retrieval systems well beyond that of lexical term matching models such as BM25. While monolingual retrieval tasks have benefited from large-scale training collections such as MS MARCO and advances in neural architectures, cross-language retrieval tasks have fallen behind these advancements. This paper introduces ColBERT-X, a generalization of the ColBERT multi-representation dense retrieval model that uses the XLM-RoBERTa (XLM-R) encoder to support cross-language information retrieval (CLIR). ColBERT-X can be trained in two ways. In zero-shot training, the system is trained on the English MS MARCO collection, relying on the XLM-R encoder for cross-language mappings. In translate-train, the system is trained on the MS MARCO English queries coupled with machine translations of the associated MS MARCO passages. Results on ad hoc document ranking tasks in several languages demonstrate substantial and statistically significant improvements of these trained dense retrieval models over traditional lexical CLIR baselines.
The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We describe an efficient algorithm to find the maximum likelihood estimator. The method is contrasted with the ordinary least squares approach in a simulation study, and the method is illustrated on a realistic data set.
Rankings, especially those in search and recommendation systems, often determine how people access information and how information is exposed to people. Therefore, how to balance the relevance and fairness of information exposure is considered as one of the key problems for modern IR systems. As conventional ranking frameworks that myopically sorts documents with their relevance will inevitably introduce unfair result exposure, recent studies on ranking fairness mostly focus on dynamic ranking paradigms where result rankings can be adapted in real-time to support fairness in groups (i.e., races, genders, etc.). Existing studies on fairness in dynamic learning to rank, however, often achieve the overall fairness of document exposure in ranked lists by significantly sacrificing the performance of result relevance and fairness on the top results. To address this problem, we propose a fair and unbiased ranking method named Maximal Marginal Fairness (MMF). The algorithm integrates unbiased estimators for both relevance and merit-based fairness while providing an explicit controller that balances the selection of documents to maximize the marginal relevance and fairness in top-k results. Theoretical and empirical analysis shows that, with small compromises on long list fairness, our method achieves superior efficiency and effectiveness comparing to the state-of-the-art algorithms in both relevance and fairness for top-k rankings.
Leveraging biased click data for optimizing learning to rank systems has been a popular approach in information retrieval. Because click data is often noisy and biased, a variety of methods have been proposed to construct unbiased learning to rank (ULTR) algorithms for the learning of unbiased ranking models. Among them, automatic unbiased learning to rank (AutoULTR) algorithms that jointly learn user bias models (i.e., propensity models) with unbiased rankers have received a lot of attention due to their superior performance and low deployment cost in practice. Despite their differences in theories and algorithm design, existing studies on ULTR usually use uni-variate ranking functions to score each document or result independently. On the other hand, recent advances in context-aware learning-to-rank models have shown that multivariate scoring functions, which read multiple documents together and predict their ranking scores jointly, are more powerful than uni-variate ranking functions in ranking tasks with human-annotated relevance labels. Whether such superior performance would hold in ULTR with noisy data, however, is mostly unknown. In this paper, we investigate existing multivariate scoring functions and AutoULTR algorithms in theory and prove that permutation invariance is a crucial factor that determines whether a context-aware learning-to-rank model could be applied to existing AutoULTR framework. Our experiments with synthetic clicks on two large-scale benchmark datasets show that AutoULTR models with permutation-invariant multivariate scoring functions significantly outperform those with uni-variate scoring functions and permutation-variant multivariate scoring functions.
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.
In this paper, we propose a novel end-to-end neural architecture for ranking candidate answers, that adapts a hierarchical recurrent neural network and a latent topic clustering module. With our proposed model, a text is encoded to a vector representation from an word-level to a chunk-level to effectively capture the entire meaning. In particular, by adapting the hierarchical structure, our model shows very small performance degradations in longer text comprehension while other state-of-the-art recurrent neural network models suffer from it. Additionally, the latent topic clustering module extracts semantic information from target samples. This clustering module is useful for any text related tasks by allowing each data sample to find its nearest topic cluster, thus helping the neural network model analyze the entire data. We evaluate our models on the Ubuntu Dialogue Corpus and consumer electronic domain question answering dataset, which is related to Samsung products. The proposed model shows state-of-the-art results for ranking question-answer pairs.
In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on treating either each rating or each pairwise comparison as an independent instance respectively. By extending the work of (Cao et al. 2007), we cast listwise collaborative ranking as maximum likelihood under a permutation model which applies probability mass to permutations based on a low rank latent score matrix. We present a novel algorithm called SQL-Rank, which can accommodate ties and missing data and can run in linear time. We develop a theoretical framework for analyzing listwise ranking methods based on a novel representation theory for the permutation model. Applying this framework to collaborative ranking, we derive asymptotic statistical rates as the number of users and items grow together. We conclude by demonstrating that our SQL-Rank method often outperforms current state-of-the-art algorithms for implicit feedback such as Weighted-MF and BPR and achieve favorable results when compared to explicit feedback algorithms such as matrix factorization and collaborative ranking.
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