**Generative Modelling:**Implicit probabilistic models like generative adversarial nets (GANs) and variational autoencoders (VAEs) have gained popularity in recent years and have delivered impressive advances in performance. While offering substantially more modelling flexibility than prescribed probabilistic models, implicit models in general induce intractable likelihood functions and therefore cannot be trained using maximum likelihood. On the other hand, alternative training objectives have known biases; for example, GANs suffer from the well-known issues of mode collapse/dropping, vanishing gradients and training instability, which could lead to a failure to learn the underlying data distribution. We developed a method that simultaneously overcomes all three issues and show equivalence to maximum likelihood under some conditions despite not requiring the evaluation of the likelihood itself or any derived quantities. This means that, for the first time, implicit probabilistic models can be trained to maximize likelihood.

Related papers: Implicit Maximum Likelihood Estimation | Super-Resolution via Conditional IMLE

**Learning to Optimize:**While machine learning has been applied to a wide range of domains, one domain that has conspicuously been left untouched is the design of tools that power machine learning itself. In this line of work, we ask the following question: is it possible to automate the design of algorithms used in machine learning? We introduced the first framework for learning a general-purpose iterative optimization algorithm automatically. The key idea is to treat the design of an optimization algorithm as a reinforcement learning/optimal control problem and view a particular update formula (and therefore a particular optimization algorithm) as a particular policy. Finding the optimal policy then corresponds to finding the best optimization algorithm. We parameterize the update formula using a neural net and train it using reinforcement learning to avoid the problem of compounding errors. This has inspired various subsequent work on meta-learning.

Related papers: Learning to Optimize | Learning to Optimize Neural Nets

**Fast Nearest Neighbour Search:**The method of*k*-nearest neighbours is widely used in machine learning, statistics, bioinformatics and database systems. Attempts at devising fast algorithms, however, have come up against a recurring obstacle: the curse of dimensionality. Almost all exact algorithms developed over the past 40 years exhibited a time complexity that is exponential in ambient or intrinsic dimensionality, and such persistent failure in overcoming the curse of dimensionality led to conjectures that doing so is impossible. We showed that, surprisingly, this is in fact possible — we developed an exact randomized algorithm whose query time complexity is linear in ambient dimensionality and sublinear in intrinsic dimensionality. The key insight is to avoid the popular strategy of space partitioning, which we argue gives rise to the curse of dimensionality. We demonstrated a speedup of 1-2 orders of magnitude over locality-sensitive hashing (LSH).

Related papers: Fast*k*-Nearest Neighbour Search via Dynamic Continuous Indexing | Fast*k*-Nearest Neighbour Search via Prioritized DCI

- Super-Resolution via Conditional Implicit Maximum Likelihood Estimation

**Ke Li***, Shichong Peng*, Jitendra Malik

*arXiv:1810.01406*, 2018 - Implicit Maximum Likelihood Estimation (Reviews) (Slides)

**Ke Li**, Jitendra Malik

*arXiv:1809.09087*, 2018

- Learning to Optimize Neural Nets (Blog Post) (Slides)

**Ke Li**, Jitendra Malik

*arXiv:1703.00441*, 2017 - Learning to Optimize (ICLR Version) (Blog Post) (Slides)

**Ke Li**, Jitendra Malik

*arXiv:1606.01885*, 2016 and*International Conference on Learning Representations (ICLR)*, 2017

- Fast
*k*-Nearest Neighbour Search via Prioritized DCI (Talk) (Slides)

**Ke Li**, Jitendra Malik

*International Conference on Machine Learning (ICML)*, 2017 - Fast
*k*-Nearest Neighbour Search via Dynamic Continuous Indexing (Slides)

**Ke Li**, Jitendra Malik

*International Conference on Machine Learning (ICML)*, 2016

- Amodal Instance Segmentation

**Ke Li**, Jitendra Malik

*European Conference on Computer Vision (ECCV)*, 2016 - Iterative Instance Segmentation

**Ke Li**, Bharath Hariharan, Jitendra Malik

*IEEE Conference on Computer Vision and Pattern Recognition (CVPR)*, 2016

- Efficient Feature Learning using Perturb-and-MAP

**Ke Li**, Kevin Swersky, Richard Zemel

*NIPS Workshop on Perturbations, Optimization and Statistics*, 2013