We introduce a model for constructing vector representations of words by composing characters using bidirectional LSTMs. Relative to traditional word representation models that have independent vectors for each word type, our model requires only a single vector per character type and a fixed set of parameters for the compositional model. Despite the compactness of this model and, more importantly, the arbitrary nature of the form-function relationship in language, our "composed" word representations yield state-of-the-art results in language modeling and part-of-speech tagging. Benefits over traditional baselines are particularly pronounced in morphologically rich languages (e.g., Turkish).
The work in @cite_46 proposes a window-based model for word labeling. Given a vocabulary of output labels @math , the model predicts the probability of a given label @math , for word @math as @math , where @math are the input words indexed from @math to @math . The model projects each word @math into a @math -dimentional vector @math . Then, for the word to be labelled @math , the representations @math and the @math closest words @math are concatenated into a @math -dimensional vector and a linear combination is applied using the parameters in matrix @math where @math is defined as an hyperparameter that determines the dimensionality of the output of this operation. Then, a non-linearity is applied to the resulting vector, yielding vector @math . The output label can be predicted by applying a linear transformation to this vector parametrized by @math , which generates a vector with the size of the label vocabulary @math , and a softmax is applied to this vector to obtain a probability distribution over @math .
@cite_46
2406728828 1521197246 2762016725 2766371994
This paper describes our system designed for the NLPCC 2015 shared task on Chinese word segmentation WS and POS tagging for Weibo Text. We treat WS and POS tagging as two separate tasks and use a cascaded approach. Our major focus is how to effectively exploit multiple heterogeneous data to boost performance of statistical models. This work considers three sets of heterogeneous data, i.e., Weibo @math , 10K sentences, Penn Chinese Treebank 7.0 @math , 50K, and People's Daily @math , 280K. For WS, we adopt the recently proposed coupled sequence labeling to combine @math , @math , and @math , boosting F1 score from @math baseline model trained on only @math to @math @math . For POS tagging, we adopt an ensemble approach combining coupled sequence labeling and the guide-feature based method, since the three datasets have three different annotation standards. First, we convert @math into the annotation style of @math based on coupled sequence labeling, denoted by @math . Then, we merge CTB7 and @math to train a POS tagger, denoted by @math , which is further used to produce guide features on @math . Finally, the tagging F1 score is improved from 87.93 to 88.99 +1.06 . We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order- @math tensor @math of the form @math , where @math is a signal-to-noise ratio, @math is a unit vector, and @math is a random noise tensor, the goal is to recover the planted vector @math . For the case that @math has iid standard Gaussian entries, we give an efficient algorithm to recover @math whenever @math , and certify that the recovered vector is close to a maximum likelihood estimator, all with high probability over the random choice of @math . The previous best algorithms with provable guarantees required @math . In the regime @math , natural tensor-unfolding-based spectral relaxations for the underlying optimization problem break down (in the sense that their integrality gap is large). To go beyond this barrier, we use convex relaxations based on the sum-of-squares method. Our recovery algorithm proceeds by rounding a degree- @math sum-of-squares relaxations of the maximum-likelihood-estimation problem for the statistical model. To complement our algorithmic results, we show that degree- @math sum-of-squares relaxations break down for @math , which demonstrates that improving our current guarantees (by more than logarithmic factors) would require new techniques or might even be intractable. Finally, we show how to exploit additional problem structure in order to solve our sum-of-squares relaxations, up to some approximation, very efficiently. Our fastest algorithm runs in nearly-linear time using shifted (matrix) power iteration and has similar guarantees as above. The analysis of this algorithm also confirms a variant of a conjecture of Montanari and Richard about singular vectors of tensor unfoldings. Like other machine learning paradigms, multi-label learning also suffers from the curse of dimensionality problem. Multi-label dimensionality reduction can alleviate the problem but they generally ask for sufficient labeled samples. Nevertheless, we often may only have scarce labeled samples and abundant unlabeled samples. In this paper, we propose a @math emi-supervised @math ulti-label @math imensionality @math eduction based on @math ependence @math aximization approach (SMDRdm in short). SDMRdm assumes the semantic similarity and feature similarity of multi-label samples are inter-depended. SMDRdm first applies label propagation on a neighborhood graph composed with labeled and unlabeled samples to obtain the soft labels of unlabeled samples, and then measures the semantic similarity between all the training samples (including unlabeled ones) based on these soft labels and available labels of labeled samples. Next, it measures the feature similarity between samples in the subspace projected by the target projective matrix, instead of the original high-dimensional feature space. After that, it maximizes the dependence between these two types of similarities and incorporates the dependence into linear discriminant analysis to optimize the target projective matrix. Experiments on publicly accessible multi-label data sets demonstrate that SMDRdm achieves more prominent results than other related approaches across various evaluation metrics. In addition, the empirical study also shows the semantic similarity between samples derived from soft labels works better than that derived from scarce available labels. We consider the problem of learning a one-hidden-layer neural network: we assume the input @math is from Gaussian distribution and the label @math , where @math is a nonnegative vector in @math with @math , @math is a full-rank weight matrix, and @math is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. Inspired by the formula, we design a non-convex objective function @math whose landscape is guaranteed to have the following properties: 1. All local minima of @math are also global minima. 2. All global minima of @math correspond to the ground truth parameters. 3. The value and gradient of @math can be estimated using samples. With these properties, stochastic gradient descent on @math provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity result and validate the results by simulations.