We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex surrogate for general non-modular loss functions is introduced, which provides for the first time a tractable solution for loss functions that are neither super-modular nor submodular. This convex surro-gate is based on a submodular-supermodular decomposition for which the existence and uniqueness is proven in this paper. It takes the sum of two convex surrogates that separately bound the supermodular component and the submodular component using slack-rescaling and the Lov{\'a}sz hinge, respectively. It is further proven that this surrogate is convex , piecewise linear, an extension of the loss function, and for which subgradient computation is polynomial time. Empirical results are reported on a non-submodular loss based on the S{{\o}}rensen-Dice difference function, and a real-world face track dataset with tens of thousands of frames, demonstrating the improved performance, efficiency, and scalabil-ity of the novel convex surrogate.

Decision tree classifiers are a widely used tool in data stream mining. The use of confidence intervals to estimate the gain associated with each split leads to very effective methods, like the popular Hoeffding tree algorithm. From a statistical viewpoint, the analysis of decision tree classifiers in a streaming setting requires knowing when enough new information has been collected to justify splitting a leaf. Although some of the issues in the statistical analysis of Hoeffding trees have been already clarified, a general and rigorous study of confidence intervals for splitting criteria is missing. We fill this gap by deriving accurate confidence intervals to estimate the splitting gain in decision tree learning with respect to three criteria: entropy, Gini index, and a third index proposed by Kearns and Mansour. Our confidence intervals depend in a more detailed way on the tree parameters. We also extend our confidence analysis to a selective sampling setting, in which the decision tree learner adaptively decides which labels to query in the stream. We furnish theoretical guarantee bounding the probability that the classification is non-optimal learning the decision tree via our selective sampling strategy. Experiments on real and synthetic data in a streaming setting show that our trees are indeed more accurate than trees with the same number of leaves generated by other techniques and our active learning module permits to save labeling cost. In addition, comparing our labeling strategy with recent methods, we show that our approach is more robust and consistent respect all the other techniques applied to incremental decision trees.

We're hearing a lot about automated machine learning lately, inspired in part by growing demand and the shortage of data scientists. But like many innovations, automated machine learning did not simply appear out of the blue; it is the product of at least twenty years of development. Before Unica Software launched its successful suite of marketing automation software, the company's primary business was predictive analytics, with a particular focus on neural networks. In 1995, Unica introduced Pattern Recognition Workbench (PRW), a software package that used an automated grid search to optimize model tuning for neural networks. Three years later, Unica partnered with Group 1 Software (now owned by Pitney Bowes) to market Model 1, a tool that automated model selection over four different types of predictive models.

Last week this space saw much of the largest fintech funding rounds taking place outside the U.S. That trend continues this week, with some San Francisco-grown AI thrown into the mix. This week we witnessed a major push forward in the process of collaboration between financial institutions (FIs) and startups. This week's top fundraising company was part of a startup accelerator based in Hong Kong. We also found a company creating artificial intelligence capable of accurately and reliably predicting stock market trends.

Nasa has announced that it has found evidence of flowing water on Mars. Scientists have long speculated that Recurring Slope Lineae -- or dark patches -- on Mars were made up of briny water but the new findings prove that those patches are caused by liquid water, which it has established by finding hydrated salts. Several hundred camped outside the London store in Covent Garden. The 6s will have new features like a vastly improved camera and a pressure-sensitive "3D Touch" display

SpaceX made history on Friday after successfully landing its Falcon 9 rocket on a barge in the Atlantic Ocean. Images of the tall, narrow rocket gliding down onto a droneship sparked applause and screams of joy at SpaceX mission control in Hawthorne, California. It was its fifth attempt at landing the rocket upright - a feat that the company says could pave the way for cheaper space travel. Now, new footage from an onboard camera released by founder Elon Musk shows the near-perfect landing in stunning detail. After four failed bids SpaceX finally stuck the landing Friday in the Atlantic Ocean. Now, new footage from an onboard camera released by founder Elon Musk shows the near-perfect landing in stunning detail. Primary school teacher sacked over this'inappropriate' dance SNL has fun with Clinton's subway gaffe earlier this week'What the f***?': Terrified boy haunted by ghost in bedroom The liftoff at 4:43 p.m. from Cape Canaveral was the first time that SpaceX has resupplied the ISS since the company's last cargo mission in June, which ended in disaster.

Despite Italy's recent cuts in scientific research and the so-called brain drain that has cast a shadow over growth prospects for the peninsula, the country has seen some notable advances in cancer research and robotics in recent months. At Milan's renowned San Raffaele University and Research Hospital, a breakthrough in the search for blood cancer cures that may also fight other cancers is inspiring optimism among some doctors. Dr. Chiara Bonini, head of the experimental hematology unit at San Raffaele University and Research Hospital, and her team have contributed to the global buzz surrounding T-cell therapy, which involves engineering the patient's immune system to fight cancer. Bonini's team has found a way to track the T-cells that can last longest in the immune system, which they believe may lead to creating a drug that can last through a patient's lifetime and prevent cancer from returning. "I have to say, the results are really, really promising," Bonini told FoxNews.com.

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."

Nasa has announced that it has found evidence of flowing water on Mars. Scientists have long speculated that Recurring Slope Lineae -- or dark patches -- on Mars were made up of briny water but the new findings prove that those patches are caused by liquid water, which it has established by finding hydrated salts. Several hundred camped outside the London store in Covent Garden. The 6s will have new features like a vastly improved camera and a pressure-sensitive "3D Touch" display