Predicting the efficacy of a drug for a given individual, using high-dimensional genomic measurements, is at the core of precision medicine. However, identifying features on which to base the predictions remains a challenge, especially when the sample size is small. Incorporating expert knowledge offers a promising alternative to improve a prediction model, but collecting such knowledge is laborious to the expert if the number of candidate features is very large. We introduce a probabilistic model that can incorporate expert feedback about the impact of genomic measurements on the sensitivity of a cancer cell for a given drug. We also present two methods to intelligently collect this feedback from the expert, using experimental design and multi-armed bandit models. In a multiple myeloma blood cancer data set (n=51), expert knowledge decreased the prediction error by 8%. Furthermore, the intelligent approaches can be used to reduce the workload of feedback collection to less than 30% on average compared to a naive approach.

Machine learning has become pervasive in multiple domains, impacting a wide variety of applications, such as knowledge discovery and data mining, natural language processing, information retrieval, computer vision, social and health informatics, ubiquitous computing, etc. Two essential problems of machine learning are how to generate features and how to acquire labels for machines to learn. Particularly, labeling large amount of data for each domain-specific problem can be very time consuming and costly. It has become a key obstacle in making learning protocols realistic in applications. In this paper, we will discuss how to use the existing general-purpose world knowledge to enhance machine learning processes, by enriching the features or reducing the labeling work. We start from the comparison of world knowledge with domain-specific knowledge, and then introduce three key problems in using world knowledge in learning processes, i.e., explicit and implicit feature representation, inference for knowledge linking and disambiguation, and learning with direct or indirect supervision. Finally we discuss the future directions of this research topic.

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant neighborhood size unrealistic. We propose a framework for learning this local dependence based on estimating the inverse of the Cholesky factor of the covariance matrix. Penalized maximum likelihood estimation of this matrix yields a simple regression interpretation for local dependence in which variables are predicted by their neighbors. Our proposed method involves solving a convex, penalized Gaussian likelihood problem with a hierarchical group lasso penalty. The problem decomposes into independent subproblems which can be solved efficiently in parallel using first-order methods. Our method yields a sparse, symmetric, positive definite estimator of the precision matrix, encoding a Gaussian graphical model. We derive theoretical results not found in existing methods attaining this structure. In particular, our conditions for signed support recovery and estimation consistency rates in multiple norms are as mild as those in a regression problem. Empirical results show our method performing favorably compared to existing methods. We apply our method to genomic data to flexibly model linkage disequilibrium. Our method is also applied to improve the performance of discriminant analysis in sound recording classification.

Artificial intelligence (AI), machine learning (ML), and robots are the sights and sounds of science fiction books and movies. Isaac Asimov's Three Laws of Robotics, first introduced in the 1942 short story "Runaround," became the backbone for his novel I, Robot and its film adaptation (Figure 1). Although we are still far away from achieving what movie producers and sci-fi writers have envisioned, the state of AI and ML has progressed significantly. AI software has also been in use for decades but advances in ML, including the use of deep neural networks (DNNs), are making headlines in application areas like self-driving cars. The movie I, Robot has robots that should be following Asimov's Three Laws of Robotics.

A few weeks ago at the DALI Theory of GANs workshop we had a great discussion about what GANs are even useful for. Pretty much everybody agreed that generating random images from a model is not really our goal. We either want to use GANs to train conditional probabilistic models (like we do for image super-resolution or speech synthesis, or something along those lines), or as a means of unsupervised representation learning. Indeed, many papers examine the latent space representations that GANs learn. But the elephant in the room is that nobody really agrees on what unsupervised representation learning really means, and why any GAN variant should be any better or worse at it than others, whether GANs or VAEs are better for that.

In this paper we use Gaussian Process (GP) regression to propose a novel approach for predicting volatility of financial returns by forecasting the envelopes of the time series. We provide a direct comparison of their performance to traditional approaches such as GARCH. We compare the forecasting power of three approaches: GP regression on the absolute and squared returns; regression on the envelope of the returns and the absolute returns; and regression on the envelope of the negative and positive returns separately. We use a maximum a posteriori estimate with a Gaussian prior to determine our hyperparameters. We also test the effect of hyperparameter updating at each forecasting step. We use our approaches to forecast out-of-sample volatility of four currency pairs over a 2 year period, at half-hourly intervals. From three kernels, we select the kernel giving the best performance for our data. We use two published accuracy measures and four statistical loss functions to evaluate the forecasting ability of GARCH vs GPs. In mean squared error the GP's perform 20% better than a random walk model, and 50% better than GARCH for the same data.

One aspect I always enjoy about machine learning is that questions often go back to the basics. The field essentially goes into an existential crisis every dozen years--rethinking our tools and asking foundational questions such as "why neural networks" or "why generative models".1 This was a theme in my conversations during NIPS 2016 last week, where a frequent topic was on the advantages of a Bayesian perspective to machine learning. Not surprisingly, this appeared as a big discussion point during the panel at the Bayesian deep learning workshop, where many panelists were conciliatory to the use of non-Bayesian approaches. While Bayesian inference can capture uncertainty about parameters, it relies on the model being correctly specified.

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - exact Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to {the tree model} using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data.

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

Despite the promise of big data, inferences are often limited not by sample size but rather by systematic effects. Only by carefully modeling these effects can we take full advantage of the data--big data must be complemented with big models and the algorithms that can fit them. One such algorithm is Hamiltonian Monte Carlo, which exploits the inherent geometry of the posterior distribution to admit full Bayesian inference that scales to the complex models of practical interest. In this talk I will discuss the theoretical foundations of Hamiltonian Monte Carlo, elucidating the geometric nature of its scalable performance and stressing the properties critical to a robust implementation. The talk is this Thurs, 6 Apr, 1:10-2:20pm in 303 Mudd Building at Columbia.