Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on regular grids, applicable to a general set of spaces. This is helpful whenever an algorithm *explores* to reduce uncertainty, such as in active learning, Bayesian optimization, reinforcement learning, and marginalization in graphical models. To draw samples from a DPP in practice, existing literature focuses on approximate schemes of low cost, or comparably inefficient exact algorithms like rejection sampling. We point out that, for many settings of relevance to machine learning, it is also possible to draw *exact* samples from DPPs on continuous domains. We start from an intuitive example on the real line, which is then generalized to multivariate real vector spaces. We also compare to previously studied approximations, showing that exact sampling, despite higher cost, can be preferable where precision is needed.

We describe our experience in the development of a probabilistic network for the diagnosis of acute cardiopulmonary diseases. A panel of expert physicians collaborated to specify the qualitative part, that is a directed acyclic graph defining a factorization of the joint probability distribution of domain variables. The quantitative part, that is the set of all conditional probability distributions defined by each factor, was estimated in the Bayesian paradigm: we applied a special formal representation, characterized by a low number of parameters and a parameterization intelligible for physicians, elicited the joint prior distribution of parameters from medical experts, and updated it by conditioning on a dataset of hospital patient records using Markov Chain Monte Carlo simulation. Refinement was cyclically performed until the probabilistic network provided satisfactory Concordance Index values for a selection of acute diseases and reasonable inference on six fictitious patient cases. The probabilistic network can be employed to perform medical diagnosis on a total of 63 diseases (38 acute and 25 chronic) on the basis of up to 167 patient findings.

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in high dimensions, when the number of unknown signal components is similar to the number of measurements. In this work we demonstrate, when the signal distribution and the likelihood function associated with the noise are both log-concave, that optimal MMSE performance is asymptotically achievable via another M-estimation procedure. This procedure involves minimizing convex loss and regularizer functions that are nonlinearly smoothed versions of the widely applied MAP optimization problem. Our findings provide a new heuristic derivation and interpretation for recent optimal M-estimators found in the setting of linear measurements and additive noise, and further extend these results to nonlinear measurements with non-additive noise. We numerically demonstrate superior performance of our optimal M-estimators relative to MAP. Overall, at the heart of our work is the revelation of a remarkable equivalence between two seemingly very different computational problems: namely that of high dimensional Bayesian integration underlying MMSE inference, and high dimensional convex optimization underlying M-estimation. In essence we show that the former difficult integral may be computed by solving the latter, simpler optimization problem.

We introduce Delay Pruning, a simple yet powerful technique to regularize dynamic Boltzmann machines (DyBM). The recently introduced DyBM provides a particularly structured Boltzmann machine, as a generative model of a multi-dimensional time-series. This Boltzmann machine can have infinitely many layers of units but allows exact inference and learning based on its biologically motivated structure. DyBM uses the idea of conduction delays in the form of fixed length first-in first-out (FIFO) queues, with a neuron connected to another via this FIFO queue, and spikes from a pre-synaptic neuron travel along the queue to the post-synaptic neuron with a constant period of delay. Here, we present Delay Pruning as a mechanism to prune the lengths of the FIFO queues (making them zero) by setting some delay lengths to one with a fixed probability, and finally selecting the best performing model with fixed delays. The uniqueness of structure and a non-sampling based learning rule in DyBM, make the application of previously proposed regularization techniques like Dropout or DropConnect difficult, leading to poor generalization. First, we evaluate the performance of Delay Pruning to let DyBM learn a multidimensional temporal sequence generated by a Markov chain. Finally, we show the effectiveness of delay pruning in learning high dimensional sequences using the moving MNIST dataset, and compare it with Dropout and DropConnect methods.

We consider a Degree-Corrected Planted-Partition model: a random graph on $n$ nodes with two asymptotically equal-sized clusters. The model parameters are two constants $a,b > 0$ and an i.i.d. sequence of weights $(\phi_u)_{u=1}^n$, with finite second moment $\Phi^{(2)}$. Vertices $u$ and $v$ are joined by an edge with probability $\frac{\phi_u \phi_v}{n}a$ when they are in the same class and with probability $\frac{\phi_u \phi_v}{n}b$ otherwise. We prove that it is information-theoretically impossible to estimate the spins in a way positively correlated with the true community structure when $(a-b)^2 \Phi^{(2)} \leq 2(a+b)$. A by-product of our proof is a precise coupling-result for local-neighbourhoods in Degree-Corrected Planted-Partition models, which could be of independent interest.

This paper develops robust confidence intervals in high-dimensional and left-censored regression. Type-I censored regression models are extremely common in practice, where a competing event makes the variable of interest unobservable. However, techniques developed for entirely observed data do not directly apply to the censored observations. In this paper, we develop smoothed estimating equations that augment the de-biasing method, such that the resulting estimator is adaptive to censoring and is more robust to the misspecification of the error distribution. We propose a unified class of robust estimators, including Mallow's, Schweppe's and Hill-Ryan's one-step estimator. In the ultra-high-dimensional setting, where the dimensionality can grow exponentially with the sample size, we show that as long as the preliminary estimator converges faster than $n^{-1/4}$, the one-step estimator inherits asymptotic distribution of fully iterated version. Moreover, we show that the size of the residuals of the Bahadur representation matches those of the simple linear models, $s^{3/4 } (\log (p \vee n))^{3/4} / n^{1/4}$ -- that is, the effects of censoring asymptotically disappear. Simulation studies demonstrate that our method is adaptive to the censoring level and asymmetry in the error distribution, and does not lose efficiency when the errors are from symmetric distributions. Finally, we apply the developed method to a real data set from the MAQC-II repository that is related to the HIV-1 study.

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theoretical framework for multilayer spectral graph clustering of the nodes via convex layer aggregation. Under a novel multilayer signal plus noise model, we provide a phase transition analysis that establishes the existence of a critical value on the noise level that permits reliable cluster separation. The analysis also specifies analytical upper and lower bounds on the critical value, where the bounds become exact when the clusters have identical sizes. Numerical experiments on synthetic multilayer graphs are conducted to validate the phase transition analysis and study the effect of layer weights and noise levels on clustering reliability.

This Wednesday, the tech billionaire investor announced an investment in Luminance, a newly launched startup that uses artificial technology to read contracts in order help law firms with the arduous process of due diligence for mergers and acquisitions (M&A). It's not a "sexy" piece of technology, Lynch argues -- but one that has huge implications for the way we live our lives, and is indicative of a quiet revolution in artificial intelligence. What this is is probably an example of what's going to be changing a lot of things. If you can get machine technology to be reading contracts, it's going to be changing a lot of the world around us ... you're seeing the beginning of a new age." He has since founded venture capital firm Invoke Capital -- the vehicle through which the investment in Luminance was made. This week, Business Insider sat down with the investor to discuss Luminance, Brexit, his augmented reality plans, and why he likes having an "unfair advantage." Mike Lynch is an investor in Luminance -- but was also instrumental in helping create it. "The bit that makes it possible is the machine learning, and that was being done by some research people at Cambridge, and I actually have a connection because my PhD a long, long time ago was in machine learning," Lynch said. "I was introduced to them, and what they were doing looked great, but I said to them'look, you gotta go and meet some real world people.' "So they started getting real data and they met up with [law firm] Slaughter and May, and basically the machine learnt from Slaughter and May how to do these thing and at that point they made a little company. They got a CEO who is a lady who'd actually been involved in a lot of M&A deals over their career and we funded it, and it's been developing the product, and today it comes out into the bright lights of day."

In case you haven't yet managed to find the perfect social robot for your home, this is BIG-i. BIG-i is going to stare at you without blinking until you decide that you want it. Seriously though, BIG-i should get your attention if for no other reason than it's a design that's completely different (and significantly softer) than anything we've seen before. It's also mobile, with what looks to be a simple and useful if-this-then-that-style verbal programming. The Kickstarter just Kickstarted off and has already just about reached its goal, but if giant eyeballs are your thing (and let's be honest, everyone has a thing for giant eyeballs), this robot is probably worth a look.

Wealth management firm and investment bank UBS is running artificial intelligence (AI) trials with some of its richest clients. AI applications being tested include tools designed to read facial expressions and uncover clients' unconscious biases towards or against certain types of investment. The aim is to help the company's cash-rich, but time-poor, clientele to ask the right questions about their decisions, according to UBS. The move comes as little surprise. The financial services market is in the vanguard of automation, AI, machine learning and robotics at a time when many customers prefer app-based mobile banking to online or bricks-and-mortar alternatives. Several international banks plan mass software automation, including HSBC and Bank of America investment arm Merrill Edge.