Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian information, optimize this approximation using a first-order method, such as coordinate descent and employ a line search to ensure sufficient descent. Here we propose a general framework, which includes slightly modified versions of existing algorithms and also a new algorithm, which uses limited memory BFGS Hessian approximations, and provide a novel global convergence rate analysis, which covers methods that solve subproblems via coordinate descent.

We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order-$3$ tensor $T$ of the form $T = \tau \cdot v_0^{\otimes 3} + A$, where $\tau \geq 0$ is a signal-to-noise ratio, $v_0$ is a unit vector, and $A$ is a random noise tensor, the goal is to recover the planted vector $v_0$. For the case that $A$ has iid standard Gaussian entries, we give an efficient algorithm to recover $v_0$ whenever $\tau \geq \omega(n^{3/4} \log(n)^{1/4})$, and certify that the recovered vector is close to a maximum likelihood estimator, all with high probability over the random choice of $A$. The previous best algorithms with provable guarantees required $\tau \geq \Omega(n)$. In the regime $\tau \leq o(n)$, 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-$4$ sum-of-squares relaxations of the maximum-likelihood-estimation problem for the statistical model. To complement our algorithmic results, we show that degree-$4$ sum-of-squares relaxations break down for $\tau \leq O(n^{3/4}/\log(n)^{1/4})$, 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.

In support vector machine (SVM) applications with unreliable data that contains a portion of outliers, non-robustness of SVMs often causes considerable performance deterioration. Although many approaches for improving the robustness of SVMs have been studied, two major challenges remain in robust SVM learning. First, robust learning algorithms are essentially formulated as non-convex optimization problems. It is thus important to develop a non-convex optimization method for robust SVM that can find a good local optimal solution. The second practical issue is how one can tune the hyperparameter that controls the balance between robustness and efficiency. Unfortunately, due to the non-convexity, robust SVM solutions with slightly different hyper-parameter values can be significantly different, which makes model selection highly unstable. In this paper, we address these two issues simultaneously by introducing a novel homotopy approach to non-convex robust SVM learning. Our basic idea is to introduce parametrized formulations of robust SVM which bridge the standard SVM and fully robust SVM via the parameter that represents the influence of outliers. We characterize the necessary and sufficient conditions of the local optimal solutions of robust SVM, and develop an algorithm that can trace a path of local optimal solutions when the influence of outliers is gradually decreased. An advantage of our homotopy approach is that it can be interpreted as simulated annealing, a common approach for finding a good local optimal solution in non-convex optimization problems. In addition, our homotopy method allows stable and efficient model selection based on the path of local optimal solutions. Empirical performances of the proposed approach are demonstrated through intensive numerical experiments both on robust classification and regression problems.

In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem of choosing $k$ out of $p$ features in linear regression given $n$ observations. We develop a discrete extension of modern first order continuous optimization methods to find high quality feasible solutions that we use as warm starts to a MIO solver that finds provably optimal solutions. The resulting algorithm (a) provides a solution with a guarantee on its suboptimality even if we terminate the algorithm early, (b) can accommodate side constraints on the coefficients of the linear regression and (c) extends to finding best subset solutions for the least absolute deviation loss function. Using a wide variety of synthetic and real datasets, we demonstrate that our approach solves problems with $n$ in the 1000s and $p$ in the 100s in minutes to provable optimality, and finds near optimal solutions for $n$ in the 100s and $p$ in the 1000s in minutes. We also establish via numerical experiments that the MIO approach performs better than {\texttt {Lasso}} and other popularly used sparse learning procedures, in terms of achieving sparse solutions with good predictive power.