We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be noisy or even completely missing in a stochastic manner. To this end, we propose algorithms based on sub-gradient descent method, which achieve tight minimax optimal regret bounds. When necessary, these algorithms utilize properties of the underlying stochastic settings to optimize their learning rates (step sizes). These optimizations are the main factor in providing the minimax optimal performance guarantees, especially when observations are stochastically missing. However, in real world scenarios, these properties of the underlying stochastic settings may not be revealed to the optimizer. For such a scenario, we propose a blind algorithm that estimates these properties empirically in a generally applicable manner. Through extensive experiments, we show that this empirical approach is a natural combination of regular stochastic gradient descent and the minimax optimal algorithms (which work best for randomized and adversarial function sequences, respectively).

Advancements in deep learning and the availability of large-scale datasets have resulted in great progress in computer vision and natural language processing (NLP). Deep convolutional neural networks (CNNs) have enabled unprecedented improvements in classical computer vision tasks, e.g., image classification and object detection. Progress in many NLP tasks has been similarly swift. Building upon these advances, there is a push to attack new problems that enable concept comprehension and reasoning capabilities to be studied at the intersection of vision and language (V&L) understanding. There are numerous applications for V&L systems, including enabling the visually impaired to interact with visual content using language, human-computer interaction, and visual search. Human-robot collaboration would be greatly enhanced by giving robots understanding of human language to better understand the visual world.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.

This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an optimization space, where the accuracy of K-means over a random subset of the data could act as a fitness measure. The resultant optimal vector can be used as the initial centroids for K-means.

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.

The core problem in many Latent Variable Models, widely used in Unsupervised Learning is to find a latent k-simplex K in Rd given perturbed points from it, many of which lie far outside the simplex. This problem was stated in [2] as an open problem. We address this problem under two deterministic assumptions which replace varied stochastic assumptions specific to relevant individual models. Our first contribution is to show that the convex hull K' of the averages of all delta n sized subsets of data points is close to K. We call this subset-smoothing. While K' can have exponentially many vertices, it is easily seen to have a polynomial time Optimization Oracle which in fact runs in time O(nnz(data)). This is the starting point for our algorithm. The algorithm is simple: it has k stages in each of which we use the oracle to find maximum of a carefully chosen linear function over K'; the optimal x is an approximation to a new vertex of K. The simplicity does not carry over to the proof of correctness. The proof is involved and uses existing and new tools from Numerical Analysis, especially angles between singular spaces of close-by matrices. However, the simplicity of the algorithm, especially the fact the only way we use the data is to do matrix-vector products leads to the claimed time bound. This matches the best known algorithms in the special cases and is better when the input is sparse as indeed is the case in many applications. Our algorithm applies to many special cases, including Topic Models, Approximate Non-negative Matrix factorization, Overlapping community Detection and Clustering.

Question Answering (QA) naturally reduces to an entailment problem, namely, verifying whether some text entails the answer to a question. However, for multi-hop QA tasks, which require reasoning with multiple sentences, it remains unclear how best to utilize entailment models pre-trained on large scale datasets such as SNLI, which are based on sentence pairs. We introduce Multee, a general architecture that can effectively use entailment models for multi-hop QA tasks. Multee uses (i) a local module that helps locate important sentences, thereby avoiding distracting information, and (ii) a global module that aggregates information by effectively incorporating importance weights. Importantly, we show that both modules can use entailment functions pre-trained on a large scale NLI datasets. We evaluate performance on MultiRC and OpenBookQA, two multihop QA datasets. When using an entailment function pre-trained on NLI datasets, Multee outperforms QA models trained only on the target QA datasets and the OpenAI transformer models. The code is available at https://github.com/StonyBrookNLP/multee.

Most machine translation systems generate text autoregressively, by sequentially predicting tokens from left to right. We, instead, use a masked language modeling objective to train a model to predict any subset of the target words, conditioned on both the input text and a partially masked target translation. This approach allows for efficient iterative decoding, where we first predict all of the target words non-autoregressively, and then repeatedly mask out and regenerate the subset of words that the model is least confident about. By applying this strategy for a constant number of iterations, our model improves state-of-the-art performance levels for constant-time translation models by over 3 BLEU on average. It is also able to reach 92-95% of the performance of a typical left-to-right transformer model, while decoding significantly faster.

We perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between decision variables. For a problem instance of size $n$, the currently best known upper bound on the expected runtime is $\mathcal{O}(n\lambda\log\lambda+n^2)$ (Dang and Lehre, GECCO 2015), while a lower bound necessary to understand how the algorithm copes with variable dependencies is still missing. Motivated by this, we show that the algorithm requires a $e^{\Omega(\mu)}$ runtime with high probability and in expectation if the selective pressure is low; otherwise, we obtain a lower bound of $\Omega(\frac{n\lambda}{\log(\lambda-\mu)})$ on the expected runtime. Furthermore, we for the first time consider the algorithm on the function under a prior noise model and obtain an $\mathcal{O}(n^2)$ expected runtime for the optimal parameter settings. In the end, our theoretical results are accompanied by empirical findings, not only matching with rigorous analyses but also providing new insights into the behaviour of the algorithm.

Deep neural decision forest (NDF) achieved remarkable performance on various vision tasks via combining decision tree and deep representation learning. In this work, we first trace the decision-making process of this model and visualize saliency maps to understand which portion of the input influence it more for both classification and regression problems. We then apply NDF on a multi-task coordinate regression problem and demonstrate the distribution of routing probabilities, which is vital for interpreting NDF yet not shown for regression problems. The pre-trained model and code for visualization will be available at https://github.com/Nicholasli1995/VisualizingNDF