**Abstract: **In many cases, we cannot calculate exact gradients. This is the case if we cannot evaluate how well the model was expected to have done for different parameter values, for example if the model generates a sequence of stochastic decisions. Thus, many gradient estimators have been developed, from classical techniques from reinforcement learning to modern techniques such as the relax estimator. In e.g. meta-learning second derivative estimators have also been proposed. In this talk, I will attempt to give an overview of the properties of these techniques.

**Abstract: **The idea of equivariance to symmetry transformations provides one of the first theoretically grounded principles for neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. We extend this principle beyond global symmetries to local gauge transformations, thereby enabling the development of equivariant convolutional networks on general manifolds. We show that gauge equivariant convolutional networks give a unified description of equivariant and geometric deep learning by deriving a wide range of models as special cases of our theory. To illustrate our theory on a simple example and highlight the interplay between local and global symmetries we discuss an implementation for signals defined on the icosahedron, which provides a reasonable approximation of spherical signals. We evaluate the Icosahedral CNN on omnidirectional image segmentation and climate pattern segmentation, and find that it outperforms previous methods.

**Abstract: **We propose a novel deep learning method for local self-supervised representation learning that does not require labels nor end-to-end backpropagation but exploits the natural order in data instead. Inspired by the observation that biological neural networks appear to learn without backpropagating a global error signal, we split a deep neural network into a stack of gradient-isolated modules. Each module is trained to maximally preserve the information of its inputs using the InfoNCE bound from Oord et al. [2018]. Despite this greedy training, we demonstrate that each module improves upon the output of its predecessor, and that the representations created by the top module yield highly competitive results on downstream classiﬁcation tasks in the audio and visual domain. The proposal enables optimizing modules asynchronously, allowing large-scale distributed training of very deep neural networks on unlabelled datasets.

Abstract:

Causal inference from observational data is a vital problem, but itcomes with strong assumptions. Most methods require that we observeall confounders, variables that affect both the causal variables andthe outcome variables. But whether we have observed all confounders isa famously untestable assumption. We describe the deconfounder, a wayto do causal inference with weaker assumptions than the classicalmethods require.

How does the deconfounder work? While traditional causal methodsmeasure the effect of a single cause on an outcome, many modernscientific studies involve multiple causes, different variables whoseeffects are simultaneously of interest. The deconfounder uses thecorrelation among multiple causes as evidence for unobservedconfounders, combining unsupervised machine learning and predictivemodel checking to perform causal inference. We demonstrate thedeconfounder on real-world data and simulation studies, and describethe theoretical requirements for the deconfounder to provide unbiasedcausal estimates.

This is joint work with Yixin Wang.

[*] https://arxiv.org/abs/1805.06826

Biography

David Blei is a Professor of Statistics and Computer Science atColumbia University, and a member of the Columbia Data ScienceInstitute. He studies probabilistic machine learning, including itstheory, algorithms, and application. David has received several awardsfor his research, including a Sloan Fellowship (2010), Office of NavalResearch Young Investigator Award (2011), Presidential Early CareerAward for Scientists and Engineers (2011), Blavatnik Faculty Award(2013), ACM-Infosys Foundation Award (2013), a Guggenheim fellowship(2017), and a Simons Investigator Award (2019). He is theco-editor-in-chief of the Journal of Machine Learning Research. He isa fellow of the ACM and the IMS.

Will is one of the authors behind many great recent papers. To name a few:

- Invertible Residual Networks
- FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
- Backpropagation through the Void: Optimizing control variates for black-box gradient estimation

**Abstract: **Generative models have long been promised to benefit downstream discriminative machine learning applications such as out-of-distribution detection, adversarial robustness, uncertainty quantification, semi-supervised learning and many others. Yet, except for a few notable exceptions, methods for these tasks based on generative models are considerably outperformed by hand-tailored methods for each specific task. In this talk, I will advocate for the incorporation of energy-based generative models into the standard discriminative learning framework. Energy-Based Models (EBMs) can be much more easily incorporated into discriminative models than alternative generative modeling approaches and can benefit from network architectures designed for discriminative performance. I will present a novel method for jointly training EBMs alongside classifiers and demonstrate that this approach allows us to build models which rival the performance of state-of-the-art generative models and discriminative models within a single model. Further, we demonstrate our joint model gains many desirable properties such as a built-in mechanism for out-of-distribution detection, improved calibration, and improved robustness to adversarial examples — rivaling or improving upon hand-designed methods for each task.

**Abstract: **In this talk we will discuss a few proposed approaches to learning approximate equivariance directly from data. These approaches range from weakly supervised to fully unsupervised, relying on either mutual information bounds or inductive biases respectively. Critical discussion will be encouraged as much of the work is in early phases. Preliminary results will be shown to demonstrate validity of concepts.

**Abstract: **This talk will discuss Bayesian approaches to solving the sparse signal recovery problem. In particular, methods based on priors that admit a scale mixture representation will be discussed with emphasis on Gaussian scale mixture modeling. In the context of MAP estimation, iterative reweighted approaches will be developed. The scale mixture modeling naturally leads a hierarchical framework and empirical Bayesian methods motivated by this hierarchy will be highlighted. The pros and cons of the two approaches, MAP versus Empirical Bayes, will be a subject of discussion.

**Abstract: **The problem of creating data representations can be
formulated as the definition of an encoding function which maps
observations into a predefined code space. Whenever the encoding is used
as an intermediate step for a predictive task, among the possible
encodings, we are generally interested in the ones that retain the
desired target information. Furthermore, recent literature has shown
that discarding irrelevant factors of variation in the data (minimality)
yield robustness and invariance to nuisances of the task. Following
these two general guidelines, in this work, we introduce an
information-theoretical method that exploits some known properties of
the predictive task to create robust data representations without
requiring direct supervision signals. By exploiting pairs of joint
observations, our model learns representations that are as
discriminative as the original data for the predictive task while being
more robust than the raw-signal. The proposed theory builds upon
well-known self-supervised algorithms (such as Contrastive Predictive
Coding and the InfoMax principle), bridging the gap between information
bottleneck and probabilistic invariance. Empirical evidence shows the
applicability of our model for both multi-view and single-view datasets.

**Abstract:** Deep learning has shown remarkable results for image analysis and is expected to aid individual treatment decisions in health care. Treatment recommendations are predictions with an inherently causal interpretation. To use deep learning for these applications, deep learning methods must be promoted from the level of mere associations to causal questions. We present a scenario with real-world medical images (CT-scans of lung cancers) and simulated outcome data. Through the data simulation scheme, the images contain two distinct factors of variation that are associated with survival, but represent a collider (tumor size) and a prognostic factor (tumor heterogeneity) respectively. We show that when this collider can be quantified, unbiased individual prognosis predictions are attainable with deep learning. This is achieved by (1) setting a dual task for the network to predict both the outcome and the collider and (2) enforcing a form of independence of the activation distributions of the last layer. Our method provides an example of combining deep learning and structural causal models to achieve unbiased individual prognosis predictions. Extensions of machine learning methods for applications to causal questions are required to attain the long standing goal of personalized medicine supported by artificial intelligence.

**Abstract: **Scientific imaging techniques such as optical and
electron microscopy and computed tomography (CT) scanning are used to
study the 3D structure of an object through 2D observations. These
observations are related to the original 3D object through orthogonal
integral projections. For common 3D reconstruction algorithms,
computational efficiency requires the modeling of the 3D structures to
take place in Fourier space by applying the Fourier slice theorem. At
present, it is unclear how to differentiate through the projection
operator, and hence current learning algorithms can not rely on gradient
based methods to optimize 3D structure models. In this paper we show
how back-propagation through the projection operator in Fourier space
can be achieved. We demonstrate the validity of the approach with
experiments on 3D reconstruction of proteins. We further extend our
approach to learning probabilistic models of 3D objects. This allows us
to predict regions of low sampling rates or estimate noise. A higher
sample efficiency can be reached by utilizing the learned uncertainties
of the 3D structure as an unsupervised estimate of the model fit.
Finally, we demonstrate how the reconstruction algorithm can be extended
with an amortized inference scheme on unknown attributes such as object
pose. Through empirical studies we show that joint inference of the 3D
structure and the object pose becomes more difficult when the ground
truth object contains more symmetries. Due to the presence of for
instance (approximate) rotational symmetries, the pose estimation can
easily get stuck in local optima, inhibiting a fine-grained high-quality
estimate of the 3D structure.