While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention.

Radial Basis Function (RBF) Networks, also known as networks of locally-tuned processing units (see [6]) are well known for their ease of use. Most algorithms used to train these types of net(cid:173) works, however, require a fixed architecture, in which the number of units in the hidden layer must be determined before training starts. The RCE training algorithm, introduced by Reilly, Cooper and Elbaum (see [8]), and its probabilistic extension, the P-RCE algorithm, take advantage of a growing structure in which hidden units are only introduced when necessary. The nature of these al(cid:173) gorithms allows training to reach stability much faster than is the case for gradient-descent based methods. Unfortunately P-RCE networks do not adjust the standard deviation of their prototypes individually, using only one global value for this parameter.

Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on hard-coded rules derived from empirical testing on a large heterogeneous corpora of benchmark instances might lead to sub-optimal performance. In this work, we propose an online learning approach that adapts the application of heuristics towards the single instance at hand. We replace the commonly used static heuristic handling with an adaptive framework exploiting past observations about the heuristic's behavior to make future decisions. In particular, we model the problem of controlling Large Neighborhood Search and Diving - two broad and complex classes of heuristics - as a multi-armed bandit problem. Going beyond existing work in the literature, we control two different classes of heuristics simultaneously by a single learning agent. We verify our approach numerically and show consistent node reductions over the MIPLIB 2017 Benchmark set. For harder instances that take at least 1000 seconds to solve, we observe a speedup of 4%.

Since MIP linear problems include both continuous and integer variables, they are proved to belong to the NP-hard class (see [38] for a more detailed analysis), meaning that they are not solvable in polynomial time. The complete exploration of the integer feasible set, whose cardinality grows exponentially with the number of variables, is yet possible to achieve the optimal solution, but for most of the practically significant instances, it would require unacceptable computational effort. In fact, the only way to solve to optimality any mixed-integer problem is to apply some of the well-known Branch and Bound techniques. However, despite combinatorial optimization community provided a great deal of these algorithms, for which the reader should refer to [31, 34, 16], MIP problems complexity is inherent with their belonging to NP-hard class. Therefore, when tackling MIP problems, one either seeks particular structures allowing to bring down the complexity, such as the availability, for a given class of problems, of the optimal formulation or exploits cutting plane generation to dramatically reduce the feasible region dimension. However, we often encounter MIP problems without having any prior knowledge of possible structures and, thus, pursuing the globally optimal solution could be in practice impossible or inefficient, since for our purpose a sub-optimal approximation is considered to be good enough. This makes heuristics one of the most widespread and feasible ways to achieve sub-optimal solutions of MIP problems within an affordable computational time. For the purpose of highlighting the perspective of our research, we can define two classes of MIP heuristics: improvement heuristics and start heuristics.

Modern enterprises are inundated with data; however, not all data is usable as is for machine learning. Though an organization may have millions of data points, it could still have data struggles that stunt machine learning. Turning to synthetic data for machine learning can boost privacy, democratize data, minimize bias in data sets and reduce costs. More broadly, real data and synthetic data tend to be used in combination. "I can't think of any project in the AI space where you wouldn't be able to get a better outcome by leveraging synthetic data," said Kjell Carlsson, principal analyst at Forrester Research.

Data science used to be somewhat of a mystery, more of a dark art than a repeatable, scientific process. Companies basically entrusted powerful priests called data scientists to build magical algorithms that used data to make predictions, usually to boost profits or improve customer happiness. But in recent years, the field has matured to a remarkable degree, and that is enabling progress to be made on multiple fronts, from ModelOps and reproducibility to ethics and accountability. About five years ago, the worldwide scientific community was suffering a "reproducibility crises" that impacted a wide range of scientific endeavors, including so-called hard sciences like physics and chemistry. One of the hallmarks of the scientific method is that experiments must be reproducible and will give the same results, but that lofty goal too often was not met.

The Second International Symposium on Intelligent Data Analysis (IDA97) was held at Birkbeck College, University of London, on 4 to 6 August 1997. The main theme of IDA97 was to reason about how to analyze data,perhaps as human analysts do, by exploiting many methods from diverse disciplines. This article outlines several key issues and challenges, discusses how they were addressed at the conference, and presents opportunities for further work in the field.

Networks of this type have a single layer of units with a selective response for some range of the input variables. Earn unit has an overall response function, possibly a Gaussian: D_("')

Networks of this type have a single layer of units with a selective response for some range of the input variables. Earn unit has an overall response function, possibly a Gaussian: D_("')

Networks of this type have a single layer of units with a selective response for some range of the input variables.