In this paper we address the problem of forecasting the target events of a time series given the distribution
The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet.
Nowadays investors are facing changing conditions of global financial markets and should evaluate risks correctly. The most crucial factor is market risk that defines financial stability and investment results of professional participants at financial market and its clients. One of the characteristics of American stocks are higher volatility during financial report announcements. Common VaR methodology doesn’t take this into consideration as it lowers volatility during such periods and lowers it in other cases. Thereby a more flexible HVD-VaR model is proposed that allows risk estimation for each period separately. This can be possible due to the fact that announcement days are predefined. The proposed methodology is effective for a half of S&P500 stocks, so it’s useful for several financial instruments AS a result a more precise risk estimation method is proposed that considers extreme price movements caused by earnings announcement.
Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a new class of statistical procedures for market graph identification was introduced and the optimality of these procedures in the Pearson correlation Gaussian network was proved. However, the procedures obtained have a high reliability only for Gaussian multivariate distributions of stock attributes. One of the ways to correct this problem is to consider different networks generated by different measures of pairwise similarity of stocks. A new and promising model in this context is the sign similarity network. In this paper the market graph identification problem in the sign similarity network is reviewed. A new class of statistical procedures for the market graph identification is introduced and the optimality of these procedures is proved. Numerical experiments reveal an essential difference in the quality between optimal procedures in sign similarity and Pearson correlation networks. In particular, it is observed that the quality of the optimal identification procedure in the sign similarity network is not sensitive to the assumptions on the distribution of stock attributes.
Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conventional training. We also show that this Stochastic Weight Averaging (SWA) procedure finds much broader optima than SGD, and approximates the recent Fast Geometric Ensembling (FGE) approach with a single model. Using SWA we achieve notable improvement in test accuracy over conventional SGD training on a range of state-of-the-art residual networks, PyramidNets, DenseNets, and ShakeShake networks on CIFAR-10, CIFAR-100, and ImageNet. In short, SWA is extremely easy to implement, improves generalization, and has almost no computational overhead.
A Gaussian graphical model is a graphical representation of the dependence structure for
a Gaussian random vector. Gaussian graphical model selection is a statistical problem that
identifies the Gaussian graphical model from observations. There are several statistical
approaches for Gaussian graphical model identification. Their properties, such as unbiasedeness
and optimality, are not established. In this paper we study these properties.
We consider the graphical model selection problem in the framework of multiple decision
theory and suggest assessing these procedures using an additive loss function. Associated
risk function in this case is a linear combination of the expected numbers of the two types
of error (False Positive and False Negative). We combine the tests of a Neyman structure for
individual hypotheses with simultaneous inference and prove that the obtained multiple
decision procedure is optimal in the class of unbiased multiple decision procedures.
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).