We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing empirical dependence measures as an objective function in both deflation and parallel manners. Solving this minimization problem, we introduce Latin hypercube sampling (LHS) (McKay et al., 2000), and a global optimization method, Bayesian optimization (BO) (Mockus, 1994) to improve the initialization of the Newton-type local optimization method. The performance of MDMICA is evaluated in various simulation studies and an image data example. When the ICA model is correct, MDMICA achieves competitive results compared to existing approaches. When the ICA model is misspecified, the estimated independent components are less mutually dependent than the observed components using MDMICA, while they are prone to be even more mutually dependent than the observed components using other approaches.

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two-block coordinate descent algorithms tackling the non-convex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms, namely, accelerated hierarchical alternating least squares (A-HALS) and alternating nonnegative least squares (ANLS), using synthetic, image and document data sets.

Recent work has managed to learn cross-lingual word embeddings without parallel data by mapping monolingual embeddings to a shared space through adversarial training. However, their evaluation has focused on favorable conditions, using comparable corpora or closely-related languages, and we show that they often fail in more realistic scenarios. This work proposes an alternative approach based on a fully unsupervised initialization that explicitly exploits the structural similarity of the embeddings, and a robust self-learning algorithm that iteratively improves this solution. Our method succeeds in all tested scenarios and obtains the best published results in standard datasets, even surpassing previous supervised systems. Our implementation is released as an open source project at https://github.com/artetxem/vecmap

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community. The goal of this paper is to show how the dominant eigenfunctions of these operators in combination with gradient-based optimization techniques can be used to detect long-lived coherent patterns in high-dimensional time-series data. The results will be illustrated using video data and a fluid flow example.

The analysis of complex systems such as inventory control, financial markets, waste-to-energy plants and computer networks is difficult because of the inherent uncertainties in these systems. Risk-aware optimization offers a possible remedy by giving stronger reliability guarantees than the risk-neutral case. Furthermore, it allows expression of the risk attitude of the decision maker. Risk awareness is especially important in sequential decision making because of the dynamic nature of the uncertainty. Markov decision processes (MDPs) introduced by Bellman in [10] provide a mathematical framework for modeling sequential decision making in situations where outcomes are partly random and partly under the control the decision maker. However, in many cases the exact model of the underlying Markov decision process is not known and one can only observe the trajectory of states, actions, and rewards/costs.

We present a simple model of a non-equilibrium self-organizing market where asset prices are partially driven by investment decisions of a bounded-rational agent. The agent acts in a stochastic market environment driven by various exogenous "alpha" signals, agent's own actions (via market impact), and noise. Unlike traditional agent-based models, our agent aggregates all traders in the market, rather than being a representative agent. Therefore, it can be identified with a bounded-rational component of the market itself, providing a particular implementation of an Invisible Hand market mechanism. In such setting, market dynamics are modeled as a fictitious self-play of such bounded-rational market-agent in its adversarial stochastic environment. As rewards obtained by such self-playing market agent are not observed from market data, we formulate and solve a simple model of such market dynamics based on a neuroscience-inspired Bounded Rational Information Theoretic Inverse Reinforcement Learning (BRIT-IRL). This results in effective asset price dynamics with a non-linear mean reversion - which in our model is generated dynamically, rather than being postulated. We argue that our model can be used in a similar way to the Black-Litterman model. In particular, it represents, in a simple modeling framework, market views of common predictive signals, market impacts and implied optimal dynamic portfolio allocations, and can be used to assess values of private signals. Moreover, it allows one to quantify a "market-implied" optimal investment strategy, along with a measure of market rationality. Our approach is numerically light, and can be implemented using standard off-the-shelf software such as TensorFlow.

Embedding representation learning via neural networks is at the core foundation of modern similarity based search. While much effort has been put in developing algorithms for learning binary hamming code representations for search efficiency, this still requires a linear scan of the entire dataset per each query and trades off the search accuracy through binarization. To this end, we consider the problem of directly learning a quantizable embedding representation and the sparse binary hash code end-to-end which can be used to construct an efficient hash table not only providing significant search reduction in the number of data but also achieving the state of the art search accuracy outperforming previous state of the art deep metric learning methods. We also show that finding the optimal sparse binary hash code in a mini-batch can be computed exactly in polynomial time by solving a minimum cost flow problem. Our results on Cifar-100 and on ImageNet datasets show the state of the art search accuracy in precision@k and NMI metrics while providing up to 98X and 478X search speedup respectively over exhaustive linear search.

Gradient-based optimization methods are the most popular choice for finding local optima for classical minimization and saddle point problems. Here, we highlight a systemic issue of gradient dynamics that arise for saddle point problems, namely the presence of undesired stable stationary points that are no local optima. We propose a novel optimization approach that exploits curvature information in order to escape from these undesired stationary points. We prove that different optimization methods, including gradient method and adagrad, equipped with curvature exploitation can escape non-optimal stationary points. We also provide empirical results on common saddle point problems which confirm the advantage of using curvature exploitation.

Modern information processing systems generate massive datasets which are often strongly heterogeneous, e.g., partially labeled mixtures of different media (audio, video, text). A quite successful approach to such datasets is based on representing the data as networks or graphs. In particular, we represent datasets by graph signals defined over an underlying graph, which reflects similarities between individual data points. The graph signal values encode label information which often conforms to a clustering hypothesis, i.e., the signal values (labels) of close-by nodes (similar data points) are similar. Two core problems considered within graph signal processing (GSP) are (i) how to sample them, i.e., which signal values provide the most information about the entire dataset, and (ii) how to recover the entire graph signal from these few signal values (samples). These problems have been studied in [1]-[6] which discussed convex optimization methods for recovering a graph signal from a small number of signal values observed on the nodes belonging to a given (small) sampling set. Sufficient conditions on the sampling set and clustering structure such that these convex methods are successful have been discussed in [4], [7].

We examine the squared error loss landscape of shallow linear neural networks. By utilizing a regularizer on the training samples, we show---with significantly milder assumptions than previous works---that the corresponding optimization problems have benign geometric properties: there are no spurious local minima and the Hessian at every saddle point has at least one negative eigenvalue. This means that at every saddle point there is a directional negative curvature which algorithms can utilize to further decrease the objective value. These geometric properties imply that many local search algorithms---including gradient descent, which is widely utilized for training neural networks---can provably solve the training problem with global convergence. The additional regularizer has no effect on the global minimum value; rather, it plays a useful role in shrinking the set of critical points. Experiments show that this additional regularizer also speeds the convergence of iterative algorithms for solving the training optimization problem in certain cases.