We prove its consistency and show that the asymptotic variance ofitssolution canattaintheequality oftheefficiencybound undermild regularity conditions.

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating the likelihood function which may not be tractable due to the normalization term of the density model. In this paper, we derive a Discriminative Likelihood Estimator (DLE) from the Kullback-Leibler divergence minimization criterion implemented via density ratio estimation and a Stein operator. We study the problem of model inference using DLE. We prove its consistency and show that the asymptotic variance of its solution can attain the equality of the efficiency bound under mild regularity conditions. We also propose a dual formulation of DLE which can be easily optimized. Numerical studies validate our asymptotic theorems and we give an example where DLE successfully estimates an intractable model constructed using a pre-trained deep neural network.

Neural Information Processing Systems http://nips.cc/

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating the likelihood function which may not be tractable due to the normalization term of the density model. In this paper, we derive a Discriminative Likelihood Estimator (DLE) from the Kullback-Leibler divergence minimization criterion implemented via density ratio estimation and a Stein operator. We study the problem of model inference using DLE.

We present the "Spanish Built Factual Freectianary 2.0" (Spanish-BFF-2) as the second iteration of an AI-generated Spanish dictionary. Previously, we developed the inaugural version of this unique free dictionary employing GPT-3. In this study, we aim to improve the dictionary by using GPT-4-turbo instead. Furthermore, we explore improvements made to the initial version and compare the performance of both models.

Dictionaries are one of the oldest and most used linguistic resources. Building them is a complex task that, to the best of our knowledge, has yet to be explored with generative Large Language Models (LLMs). We introduce the "Spanish Built Factual Freectianary" (Spanish-BFF) as the first Spanish AI-generated dictionary. This first-of-its-kind free dictionary uses GPT-3. We also define future steps we aim to follow to improve this initial commitment to the field, such as more additional languages.

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating the likelihood function which may not be tractable due to the normalization term of the density model. In this paper, we derive a Discriminative Likelihood Estimator (DLE) from the Kullback-Leibler divergence minimization criterion implemented via density ratio estimation and a Stein operator. We study the problem of model inference using DLE.

Many real life applications brought by modern technologies often have multiple data sources, which are usually characterized by both attributes and pairwise similarities at the same time. For example in webpage ranking, a webpage is usually represented by a vector of term values, and meanwhile the internet linkages induce pairwise similarities among the webpages. Although both attributes and pairwise similarities are useful for class membership inference, many traditional embedding algorithms only deal with one type of input data. In order to make use of the both types of data simultaneously, in this work, we propose a novel Discriminant Laplacian Embedding (DLE) approach. Supervision information from training data are integrated into DLE to improve the discriminativity of the resulted embedding space. By solving the ambiguity problem in computing the scatter matrices caused by data points with multiple labels, we successfully extend the proposed DLE to multi-label classification. In addition, through incorporating the label correlations, the classification performance using multi-label DLE is further enhanced. Promising experimental results in extensive empirical evaluations have demonstrated the effectiveness of our approaches.