This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic methods. In contrast to traditional methods that attempt to solve the ERM problem corresponding to the full dataset directly, adaptive sample size schemes start with a small number of samples and solve the corresponding ERM problem to its statistical accuracy. The sample size is then grown geometrically -- e.g., scaling by a factor of two -- and use the solution of the previous ERM as a warm start for the new ERM. Theoretical analyses show that the use of adaptive sample size methods reduces the overall computational cost of achieving the statistical accuracy of the whole dataset for a broad range of deterministic and stochastic first-order methods. The gains are specific to the choice of method. When particularized to, e.g., accelerated gradient descent and stochastic variance reduce gradient, the computational cost advantage is a logarithm of the number of training samples. Numerical experiments on various datasets confirm theoretical claims and showcase the gains of using the proposed adaptive sample size scheme.

One of the hardest problems, when dealing with Machine Learning algorithms, is evaluating whether the trained model performs well with unseen samples. For example, it may happen that a model behaves very well with a given dataset, but it is not able to predict the correct values, when deployed. This discordance between the trained and testing data can be due to different problems. One of the most common problems is overfitting. A model thats fits the training set well but testing set poorly is said to be overfit to the training set and a model that fits both sets poorly is said to be underfit.

Accenture's Fintech Innovation Lab initiative is an accelerator programme designed to put the best fintech start ups in front of potential banking customers and investors - we interview those that made it to the final. Quotip: "We help to introduce investors into the financial product industry and help them find ideas in any product environment by using a machine learning based algorithm. "Traditional banks have a big trading desk for pricing products but for many it is not economical to do that in the same way. So we came up with an idea for machine learning to extract information from the exchange. "In Switzerland there are lots of products listed on an exchange, if you look at them there is something like 35,000 on the Swiss exchange. We will extract information from the prices that are fed from investment banks to the exchange and with this information we can incorporate pricing and feed that back to customers."