## NIPS 2014 main meeting

NIPS is growing fast with 2400+ participants! I felt there were proportionally less “neuro” papers compared to last year, maybe because of a huge presence of deep network papers. My NIPS keywords of the year: Deep learning, Bethe approximation/partition function, variational inference, climate science, game theory, and Hamming ball. Here are my notes on the interesting papers/talks from my biased sampling by a neuroscientist as I did for the previous meetings. Other bloggers have written about the conference: Paul Mineiro, John Platt, Yisong Yue and Yun Hyokun (in Korean).

## The NIPS Experiment

The program chairs, Corinna Cortes and Neil Lawrence, ran an experiment on the reviewing process and estimated the inconsistency. 10% of the papers were chosen to be reviewed independently by two pools of reviewers and area chair, hence those authors got 6-8 reviews, and had to submit 2 author responses. The disagreement was around 25%, meaning around half of the accepted papers could have been rejected (the baseline assuming independent random acceptance was around 38%). This tells you that the variability in NIPS reviewing process is, so keep that in mind whether your papers got in or not! They accepted all papers that had disagreement between the two pools, so the overall acceptance rate was a bit higher this year. For details, see Eric Price’s blog post and Bert Huang’s post.

## Latent variable modeling of neural population activity

**Extracting Latent Structure From Multiple Interacting Neural Populations**

Joao Semedo, Amin Zandvakili, Adam Kohn, Christian K. Machens, Byron M. Yu

How can we quantify how two populations of neurons interact? A full interaction model would require O(N^2) which quickly makes the inference intractable. Therefore, low-dimensional interaction model could be useful, and this paper exactly does this by extending the ideas of canonical correlation analysis to vector autoregressive processes.

**Clustered factor analysis of multineuronal spike data**

Lars Buesing, Timothy A. Machado, John P. Cunningham, Liam Paninski

How can you put more structure to a PLDS (Poisson linear dynamical system) model? They assumed disjoint groups of neurons would have loadings from a restricted set of factors only. For application, they actually restricted the loading weights to be non-negative, in order to separate out the two underlying components of oscillation in spinal cord. They have a clever subspace clustering based initialization, and a variational inference procedure.

**A Bayesian model for identifying hierarchically organised states in neural population activity**

Patrick Putzky, Florian Franzen, Giacomo Bassetto, Jakob H. Macke

How do you capture discrete states in the brain, such as UP/DOWN states? They propose using a probabilistic hierarchical hidden Markov model for population of spiking neurons. The hierarchical structure reduces the effective number of parameters of the state transition matrix. The full model captures the population variability better than coupled GLMs, though the number of states and their structure is not learned. Estimation is via variational inference.

**On the relations of LFPs & Neural Spike Trains**

David E. Carlson, Jana Schaich Borg, Kafui Dzirasa, Lawrence Carin.

**Analysis of Brain States from Multi-Region LFP Time-Series**

Kyle R. Ulrich, David E. Carlson, Wenzhao Lian, Jana S. Borg, Kafui Dzirasa, Lawrence Carin

## Bayesian brain, optimal brain

**Fast Sampling-Based Inference in Balanced Neuronal Networks**

Guillaume Hennequin, Laurence Aitchison, Mate Lengyel

**Sensory Integration and Density Estimation**

Joseph G. Makin, Philip N. Sabes

**Optimal Neural Codes for Control and Estimation**

Alex K. Susemihl, Ron Meir, Manfred Opper

**Spatio-temporal Representations of Uncertainty in Spiking Neural Networks**

Cristina Savin, Sophie Denève

**Optimal prior-dependent neural population codes under shared input noise**

Agnieszka Grabska-Barwinska, Jonathan W. Pillow

**Neurons as Monte Carlo Samplers: Bayesian ￼Inference and Learning in Spiking Networks**

Yanping Huang, Rajesh P. Rao

## Other Computational and/or Theoretical Neuroscience

**Using the Emergent Dynamics of Attractor Networks for Computation (Posner lecture)**

J. J. Hopfield

He introduced bump attractor networks via analogy of magnetic bubble (shift register) memory. He suggested that cadence and duration variations in voice can be naturally integrated with state-dependent synaptic input. Hopfield previously suggested using relative spike timings to solve a similar problem in olfaction. Note that this continuous attractor theory predicts low-dimensional neural representation. His paper is available as a preprint.

**Deterministic Symmetric Positive Semidefinite Matrix Completion**

William E. Bishop and Byron M. Yu

See workshop posting where Will gave a talk on this topic.

## General Machine Learning

**Identifying and attacking the saddle point problem in high-dimensional non-convex optimization**

Yann N. Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, Yoshua Bengio

From results in statistical physics, they hypothesize that there are more saddles in high-dimension which are the main cause of slow convergence of stochastic gradient descent. In addition, exact Newton method converges to saddles, (stochastic) gradient descent is slow to get out of saddles, causing lengthy platou in training neural networks. They provide a theoretical justification for a known heuristic optimization method which is to take the absolute value of eigenvalues of the Hessian when taking the Newton step. This avoids saddles, and dramatically improves convergence speed.

**A* Sampling**

Chris J. Maddison, Daniel Tarlow, Tom Minka

Extends the Gumbel-Max Trick to an exact sampling algorithm for general (low-dimensional) continuous distributions with intractable normalizers. The trick involves perturbing a discrete-domain function by adding an independent samples from Gumbel distribution.They construct Gumbel process which gives bounds on the intractable log partition function, and use it to sample.

**Divide-and-Conquer Learning by Anchoring a Conical Hull**

Tianyi Zhou, Jeff A. Bilmes, Carlos Guestrin

**Spectral Learning of Mixture of Hidden Markov Models**

Cem Subakan, Johannes Traa, Paris Smaragdis

**Clamping Variables and Approximate Inference**

Adrian Weller, Tony Jebara

His slides are available online.

**Information-based learning by agents in unbounded state spaces**

Shariq A. Mobin, James A. Arnemann, Fritz Sommer

**Expectation Backpropagation: Parameter-Free Training of Multilayer Neural Networks with Continuous or Discrete Weights**

Daniel Soudry, Itay Hubara, Ron Meir

**Self-Paced Learning with Diversity**

Lu Jiang, Deyu Meng, Shoou-I Yu, Zhenzhong Lan, Shiguang Shan, Alexander Hauptmann

Last week, I co-organized the NIPS workshop titled: Large scale optical physiology: From data-acquisition to models of neural coding with Ferran Diego Andilla, Jeremy Freeman, Eftychios Pnevmatikakis and Jakob Macke. Optical neurophysiology promises larger population recordings, but we are also facing with technical challenges in hardware, software, signal processing, and statistical tools to analyze high-dimensional data. Here are highlights of some of the non-optical physiology talks:

**Surya Ganguli** presented exciting new results improving from his last NIPS workshop and last COSYNE workshop talks. Our experimental limitations put us to analyze severely subsampled data, and we often find correlations and low-dimensional dynamics. Surya asks “*How would dynamical portraits change if we record from more neurons?*” This time he had detailed results for single-trial experiments. Using matrix perturbation, random matrix, and non-commutative probability theory, they show a sharp phase transition in recoverability of the manifold. Their model was linear Gaussian, namely , where X is a low-rank neural trajectories over time, U is a sparse subsampling matrix, and Z is additive Gaussian noise. The bound for recovery had a form of , where K is the dimension of the latent dynamics, P is the temporal duration (samples), M is the number of subsampled neurons, and SNR denotes the signal-to-noise ratio of a single neuron.

**Vladimir Itskov** gave a talk about inferring structural properties of the network from the estimated covariance matrix (We originally invited his collaborator Eva Pastalkova, but she couldn’t make it due to a job interview). An undirected graph which has weights that corresponds to an embedding in an Euclidean space shows a characteristic Betti curve: curve of Betti numbers as a function of threshold for the graph’s weights which is varied to construct the topological objects. For certain random graphs, the characteristics are very different, hence they used it to quantify how ‘random’ or ‘low-dimensional’ the covariances they observed were. Unfortunately, these curves are very computationally expensive so only up to 3rd Betti number can be estimated, and the Betti curves are too noisy to be used for estimating dimensionality directly. But, they found that hippocampal data were far from ‘random’. A similar talk was given at CNS 2013.

**William Bishop**, a 5th year graduate student working with Byron Yu and Rob Kass, talked about stitching partially overlapping covariance matrices, a problem first discussed in NIPS 2013 by Srini Turaga and coworkers: *Can we estimate the full noise correlation matrix of a large population given smaller overlapping observations?* He provided sufficient conditions for stitching, the most important of which is to make the covariance matrix of the overlap at least the rank of the entire covariance matrix. Furthermore, he analyzed theoretical bounds on perturbations which can be used for designing strategies for choosing the overlaps carefully. For details see the corresponding main conference paper, Deterministic Symmetric Positive Semidefinite Matrix Completion.

Unfortunately, due to weather conditions Rob Kass couldn’t make it to the workshop.

## 9th Black Board Day (BBD9)

Every last Sunday of April, I have been organizing a small workshop called BBD. We discuss logic, math, and science on a blackboard (this year, it was actually on a blackboard unlike the past 3 years!)

The main theme was **paradox**. A paradox is a *puzzling contradiction*; using some sort of reasoning one derives two contradicting conclusions. Consistency is an essential quality of a reasoning system, that is, it should not be able to produce contradictions by itself. Therefore, true paradoxes are hazardous to the fundamentals of being rational, but fortunately, most paradoxes are only apparent and can be resolved. Today (April 27th, 2014), we had several paradoxes presented:

**Memming**: I presented the **Pinocchio paradox**, which is a fun variant of the Liar paradox. Pinocchio’s nose grows if and only if Pinocchio tells a false statement. What happens when Pinocchio says “My nose grows now”/”My nose will grow now”? It either grows or not grows. If it grows, he is telling the truth, so it should not grow. If it is false, then it should grow, but then it is true again. Our natural language allows self-referencing, but is it really logically possible? (In the incompleteness theorem, Gödel numbering allows self-referencing using arithmetic.) There are several possible resolutions, such as, Pinocchio cannot say that statement, Pinocchio’s world is inconsistent (and hence cannot have physical reality attached to it), Pinocchio cannot know the truth value, and so on. In any case, a good logical system shouldn’t be able to produce such paradoxes.

**Jonathan Pillow**, continuing on the fairy tale theme, presented the **sleeping beauty paradox**. Toss a coin, sleeping beauty will be awakened once if it is head, twice if it is tail. Every time she is awakened, she is asked “What is your belief that the coin was heads?”, and given a drug that erases the memory of this awakening, and goes back to sleep. One argument (“halfer” position) says since a priori belief was 1/2, and each awakening does not provide more evidence, her belief does not change and would answer 1/2. The argument (“thirder” position) says that you are twice more likely to be awakened for the tail toss, hence the probability should be 1/3. If a certain reward was assigned to making a correct guess, the thirder position seems to be correct probability to use as the guess, but do we necessarily have matching belief? This paradox is still under debate, have not had a full resolution yet.

**Kyle Mandi** presented the classical Zeno’s paradox where your intuition on infinite sum of finite things being infinite is challenged. He also showed Gabriel’s horn where a simple (infinite) object with finite volume, but infinite surface area is given. Hence, if you were to pour in paint in this horn, you would need finite paint, but would never be able to paint the entire surface. (Hence its nickname: painter’s paradox)

**Karin Knudson** introduced the Banach-Tarski paradox where one solid unit sphere in 3D can be decomposed into 5 pieces, and only by translation and rotation, they are reconstructed into two solid unit spheres. In general, if two uncountable sets A, B are bounded with non-empty interior in with , then one can find a finite decomposition such that each piece in A is congruent to the corresponding piece in B. It requires some group theory, non-measurable sets, and the axiom of choice (fortunately).

**Harold Gutch** told us about the Borel-Kolmogorov paradox. What is the conditional distribution on a great circle when points are uniformly distributed on the surface of a sphere? One argument says it should be uniform by symmetry. But, a simple sampling scheme in polar coordinate shows that it should be proportional to cosine of the angle. Basically, the lesson is, never take conditional probabilities on sets of measure zero (not to be confused with conditional densities). Furthermore, he told us about a formula to produce infinitely many paradoxes from Jaynes’ book (ch 15) based on ill-defined series convergences.

**Andrew Tan** presented Rosser’s extension of Gödel’s first incompleteness theorem with the statement that colloquially says “For every proof of me, there’s a shorter disproof.” For any consistent system T that contains PA (Peano axioms), there exists an , which is neither provable nor disprovable within T. Also, by the second incompleteness theorem, the consistency of PA (“con(PA)”) implies , which together with Gödel’s first incompleteness theorem that is neither provable nor disprovable within PA, implies that PA augmented with “con(PA)” or “not con(PA)” are both consistent. However, the latter is paradoxical, since it appears that a consistent system declares its own inconsistency, and the natural number system that we are familiar with is not a model for the system. But, it could be resolved by creating a non-standard model of arithmetic. References: [V. Gitman’s blog post and talk slides][S. Reid, arXiv 2013]

I had a wonderful time, and I really appreciate my friends for joining me in this event!

## Lobster olfactory scene analysis

Recently, there was a press release and a youtube video from University of Florida about one of my recent papers on neural code in the lobster olfactory system, and also by others [e.g. 1, 2, 3, 4]. I decided to write a bit about it in my own perspective. In general, I am interested in understanding how neurons process and represent information in their output through which they communicate with other neurons and collectively compute. In this paper, we show how a subset of olfactory neurons can be used like a stop watch to measure temporal patterns of smell.

Unlike vision and audition, the olfactory world is perceived through a filament of odor plume riding on top of complex and chaotic turbulence. Therefore, you are not going to be in constant contact with the odor (say the scent of freshly baked chocolate chip cookies) while you search for the source (cookies!). You might not even smell it at all for a long periods of time, even if the target is nearby depending on the air flow. Dogs are well known to be good at this task, and so are many animals. We study lobsters. Lobsters heavily rely on olfaction to track, avoid, and detect odor sources such as other lobsters, predators, and food, therefore, it is important for them to constantly analyze olfactory sensory information to put together an olfactory scene. In auditory system, the miniscule temporal differences in sound arriving to each of your ears is a critical cue for estimating the direction of the sound source. Similarly, one critical component for olfactory scene analysis is the *temporal* structure of the odor pattern. Therefore, we wanted to find out how neurons encode and process this information.

The neurons we study are of a subtype of olfactory sensory neurons. Sensory neurons detect signals, encode them into a temporal pattern of activity, so that it can be processed by downstream neurons. Thus, it was very surprising when we (Dr. Yuriy Bobkov) found that those neurons were spontaneously generating signals–in the form of regular bursts of action potentials–even in the absence of odor stimuli [Bobkov & Ache 2007]. We were wondering why a sensory system would generate its own signal, because the downstream neurons would not know if the signal sent by these neurons are caused by external odor stimuli (smell), or are spontaneously generated. However, we realized that they can work like little clocks. When external odor molecules stimulate the neuron, it sends a signal in a time dependent manner. Each neuron is too noisy to be a precise clock, but there is a whole population of these neurons, such that together they can measure the temporal aspects critical for the olfactory scene analysis. The temporal aspects, combined with other cues such as local flow information and navigation history, in turn can be used to track targets and estimate distances to sources. Furthermore, this temporal memory was previously believed to be formed in the brain, but our results suggest a simple yet effective mechanism in the very front end, the sensors themselves.

**Applications**: Currently electronic nose technology is mostly focused on discriminating ‘what’ the odor is. We bring to the table how animals might use the ‘when’ information to reconstruct the ‘where’ information, putting together an olfactory scene. Perhaps it could inspire novel search strategies for odor tracking robots. Another possibility is to build neuromorphic chips that emulate artificial neurons using the same principle to encode temporal patterns into instantaneously accessible information. This could be a part of low-power sensory processing unit in a robot. The principle we found are likely not limited to lobsters and could be shared by other animals and sensory modality.

EDIT: There’s an article on the analytical scientist about this paper.

**References**:

- Bobkov, Y. V. and Ache, B. W. (2007). Intrinsically bursting olfactory receptor neurons.
*J Neurophysiol*, 97(2):1052-1057. - Park, I. M., Bobkov, Y. V., Ache, B. W., and Príncipe, J. C. (2014). Intermittency coding in the primary olfactory system: A neural substrate for olfactory scene analysis.
*The Journal of Neuroscience*, 34(3):941-952. [pdf]

This work by I. Memming Park is licensed under a Creative Commons Attribution 4.0 International License.

## Scalable models workshop recap

Evan and I wrote a summary of the COSYNE 2014 workshop we organized!

Originally posted on Scalable models for high-dimensional neural data:

[ This blog post is collaboratively written by Evan and Memming ]

The Scalable Models workshop was a remarkable success! It attracted a huge crowd from the wee morning hours till the 7:30 pm close of the day. We attracted so much attention that we had to relocate from our original (tiny) allotted room (Superior A) to a (huge) lobby area (Golden Cliff). The talks offered both philosophical perspectives and methodological aspects, reflecting diverse viewpoints and approaches to high-dimensional neural data. Many of the discussions continued the next day in our sister workshop. Here we summarize each talk:

### Konrad Körding – Big datasets of spike data: why it is coming and why it is useful

Konrad started off the workshop by posting some philosophical questions about how big data might change the way we do science. He argued that neuroscience is rife with theories (for instance, how uncertainty is…

View original 1,677 more words

## A guide to discrete entropy estimators

Shannon’s entropy is the fundamental building block of information theory – a theory of communication, compression, and randomness. Entropy has a very simple definition, , where is the probability of i-th symbol. However, estimating entropy from observations is surprisingly difficult, and is still an active area of research. Typically, one does not have enough samples compared to the number of possible symbols (so called “undersampled regime”), there’s no unbiased estimator [Paninski 2003], and the convergence rate of a consistent estimator could be arbitrarily slow [Antos and Kontoyiannis, 2001]. There are many estimators that aim to overcome these difficulties to some degree. Deciding which estimator to use can be overwhelming, so here’s my recommendation in the form of a flow chart:

Let me explain one by one. First of all, if you have continuous (analogue) observation, read the title of this post. CDM, PYM, DPM, NSB are Bayesian estimators, meaning that they have explicit probabilistic assumptions. Those estimators provide posterior distributions or credible intervals as well as point estimates of entropy. Note that the assumptions made by these estimators do not have to be valid to make them good entropy estimators. In fact, even if they are in the wrong class, these estimators are consistent, and often give reasonable answers even in the undersampled regime.

Nemenman-Shafee-Bialek (**NSB**) uses a mixture of Dirichlet prior to have an approximately uninformative implied prior on entropy. This reduces the bias of estimator significantly for the undersampled regime, because a priori, it could have any entropy.

Centered Dirichlet mixture (**CDM**) is a Bayesian estimator with a special prior designed for binary observations. It comes in two flavors depending if your observation is close to independent (DBer) or the total number of 1’s is a good summary statistic (DSyn).

Pitman-Yor mixture (**PYM**) and Dirichlet process mixture (DPM) are for infinite or unknown number of symbols. In many cases, natural data have a vast number of possible symbols, as in the case of species samples or language, and have power-law (or scale-free) distributions. Power-law tails can hide a lot of entropy in their tails, in which case PYM is recommended. If you expect an exponentially decaying tail probabilities when sorted, then DPM is appropriate. See my previous post for more.

Non-Bayesian estimators come in many different flavors:

Best upper bound (**BUB**) estimator is a bias correction method which bounds the maximum error in entropy estimation.

Coverage-adjusted estimator (**CAE**) uses the Good-Turing estimator for the “coverage” (1 – unobserved probability mass), and uses a Horvitz-Thompson estimator for entropy in combination.

James-Stein (**JS**) estimator regularizes entropy by estimating a mixture of uniform distribution and the empirical histogram with the James-Stein shrinkage. The main advantage of JS is that it also produces an estimate of the distribution.

**Unseen** estimator uses a Poissonization of fingerprint and linear programming to find the likely underlying fingerprint, and use the entropy as an estimate.

Other notable estimators include (1) a bias correction method by Panzeri & Travis (1995) which has been popular for a long time, (2) Grassberger estimator, and (3) asymptotic expansion of NSB that only works in extremely undersampled regime and is inconsistent [Nemenman 2011]. These methods are faster than the others, if you need speed.

There are many software packages available out there. Our estimators CDMentropy and PYMentropy are implemented for MATLAB with BSD license (by now you surely noticed that this is a shameless self-promotion!). For R, some of these estimators are implemented in a package called entropy (in CRAN; written by the authors of JS estimator). There’s also a python package called pyentropy. Targeting a more neuroscience specific audience, Spike Train Analysis Toolkit contains a few of estimators implemented in MATLAB/C.

**References**

- A. Antos and I. Kontoyiannis. Convergence properties of functional estimates for discrete distributions. Random Structures & Algorithms, 19(3-4):163–193, 2001.
- E. Archer*, I. M. Park*, and J. Pillow. Bayesian estimation of discrete entropy with mixtures of stick-breaking priors. In P. Bartlett, F. Pereira, C. Burges, L. Bottou, and K. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 2024–2032. MIT Press, Cambridge, MA, 2012. [
**PYMentropy**] - E. Archer*, I. M. Park*, J. Pillow. Bayesian Entropy Estimation for Countable Discrete Distributions. arXiv:1302.0328, 2013. [
**PYMentropy**] - E. Archer, I. M. Park, and J. Pillow. Bayesian entropy estimation for binary spike train data using parametric prior knowledge. In C.J.C. Burges and L. Bottou and M. Welling and Z. Ghahramani and K.Q. Weinberger}, editors, Advances in Neural Information Processing Systems 26, 2013. [
**CDMentropy**] - A. Chao and T. Shen. Nonparametric estimation of Shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003. [
**CAE**] - P. Grassberger. Estimating the information content of symbol sequences and efficient codes. Information Theory, IEEE Transactions on, 35(3):669–675, 1989.
- J. Hausser and K. Strimmer. Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks. The Journal of Machine Learning Research, 10:1469–1484, 2009. [
**JS**] - I. Nemenman. Coincidences and estimation of entropies of random variables with large cardinalities. Entropy, 13(12):2013–2023, 2011. [
**Asymptotic NSB**] - I. Nemenman, F. Shafee, and W. Bialek. Entropy and inference, revisited. In Advances in Neural Information Processing Systems 14, pages 471–478. MIT Press, Cambridge, MA, 2002. [
**NSB**] - I. Nemenman, W. Bialek, and R. Van Steveninck. Entropy and information in neural spike trains: Progress on the sampling problem. Physical Review E, 69(5):056111, 2004. [
**NSB**] - L. Paninski. Estimation of entropy and mutual information. Neural Computation, 15:1191–1253, 2003. [
**BUB**] - S. Panzeri and A. Treves. Analytical estimates of limited sampling biases in different information measures. Network: Computation in Neural Systems, 7:87–107, 1996.
- P. Valiant and G. Valiant. Estimating the Unseen: Improved Estimators for Entropy and other Properties. In Advances in Neural Information Processing Systems 26, pp. 2157-2165, 2013. [
**UNSEEN**] - V. Q. Vu, B. Yu, and R. E. Kass. Coverage-adjusted entropy estimation. Statistics in medicine, 26 (21):4039–4060, 2007. [
**CAE**]

## NIPS 2013

This year, NIPS (Neural Information Processing Systems) had a record registration of 1900+ (it has been growing over the years) with 25% acceptance rate. This year, most of the reviews and rebuttals are also available online. I was one of the many who were live tweeting via #NIPS2013 throughout the main meeting and workshops.

Compared to previous years, it seemed like there were less machine learning in the invited/keynote talks. Also I noticed more industrial engagements (Zuckerberg from facebook was here (also this), and so was the amazon drone) as well as increasing interest in neuroscience. My subjective list of trendy topics of the meeting are **low-dimension, deep learning (and drop out), graphical model, theoretical neuroscience, computational neuroscience, big data, online learning, one-shot learning, calcium imaging**. Next year, NIPS will be at Montreal, Canada.

I presented 3 papers in the main meeting (hence missed the first two days of poster session), and attended 2 workshops (High-Dimensional Statistical Inference in the Brain, Acquiring and analyzing the activity of large neural ensembles; Terry Sejnowski gave the first talk in both). Following are the talks/posters/papers that I found interesting as a computational neuroscientist / machine learning enthusiast.

## Theoretical Neuroscience

**Neural Reinforcement Learning** (Posner lecture)

Peter Dayan

He described how theoretical quantities in reinforcement learning such as TD-error correlate with neuromodulators such as dopamine. Then he went on to Q (max) and SARSA (mean) learning rules. The third point of the talk was the difference between model-based vs model-free reinforcement learning. Model-based learning can use how the world (state) is organized and plan accordingly, while model-free learns values associated with each state. Human fMRI evidence shows an interesting mixture of model-based and model-free learning.

**A Memory Frontier for Complex Synapses
**Subhaneil Lahiri, Surya Ganguli

Despite its molecular complexity, most systems level neural models describe it as a scalar valued strength. Biophysical evidence suggests discrete states within the synapse and discrete levels of synaptic strength, which is troublesome because memory will be quickly overwritten for discrete/binary-valued synapses. Surya talked about how to maximize memory capacity (measured as area under the SNR over time) with synapses with hidden states over all possible Markovian models. Using the first-passage time, they ordered states, and derived an upper bound. Area is bounded by where M and N denote number of internal states per synapse and synapses, respectively. Therefore, less synapses with more internal state is better for longer memory.

**A theory of neural dimensionality, dynamics and measurement: the neuroscientist and the single neuron** (workshop)

Surya Ganguli

Several recent studies showed low-dimensional state-space of *trial-averaged* population activities (e.g., Churchland et al. 2012, Mante et al 2013). Surya asks what would happen to the PCA analysis of neural trajectories if we record from 1 billion neurons? He defines the participation ratio as a measure of dimensionality, and through a series of clever upper bounds, estimates the dimensionality of neural state-space that would capture 95% of the variance given *task complexity*. In addition, assuming incoherence (mixed or complex tuning), neural measurements can be seen as random projections of the high-dimensional space; along with low-dimensional dynamics, the data recovers the correct true dimension. He claims that in the current task designs, the neural state-space is limited by task-complexity, and we would not see higher dimensions as we increase the number of simultaneously observed neurons.

**Distributions of high-dimensional network states as knowledge base for networks of spiking neurons in the brain** (workshop)

Wolfgang Maass

In a series of papers (Büsing et al. 2011, Pecevski et al. 2011, Habenschuss et al. 2013), Maass showed how noisy spiking neural networks can perform probabilistic inferences via sampling. From Boltzmann machines (maximum entropy models) to constraint satisfaction problems (e.g. Sudoku), noisy SNN’s can be designed to sample from the posterior, and converges exponentially fast from any initial state. This is done by irreversible MCMC sampling of the neurons, and it can be generalized to continuous time and state space.

**Epigenetics in Cortex **(workshop)**
**Terry Sejnowski

Using an animal model of schizophrenia using ketamine that shows similar decreased gamma-band activity in the prefrontal cortex, and decrease in PV+ inhibitory neurons, it is known that Aza and Zeb (DNA methylation inhibitors) prevents this effect of ketamine. Furthermore, in Lister 2013, they showed a special type of DNA methylation (mCH) in the brain grows over the lifespan, coincides with synaptogenesis, and regulates gene expressions.

**Optimal Neural Population Codes for High-dimensional Stimulus Variables**

Zhuo Wang, Alan Stocker, Daniel Lee

They extend previous year’s paper to high-dimensions.

## Computational Neuroscience

**What can slice physiology tell us about inferring functional connectivity from spikes?** (workshop)

Ian Stevenson

Our ability to infer functional connectivity among neurons is limited by data. Using current-injection, he investigated exactly how much data is required for detecting synapses of various strength under the generalized linear model (GLM). He showed interesting scaling plots both in terms of (square root of) firing rate and (inverse) amplitude of the post-synaptic current.

**Hierarchical Modular Optimization of Convolutional Networks Achieves Representations Similar to Macaque IT and Human Ventral Stream** (main)

**Mechanisms Underlying visual object recognition: Humans vs. Neurons vs. machines** (tutorial)

Daniel L. Yamins*, Ha Hong*, Charles Cadieu, James J. DiCarlo

They built a model that can predict (average) activity of V4 and IT neurons in response to objects. Current computer vision methods do not perform well under high variability induced by transformation, rotation, and etc, while IT neuron response seems to be quite invariant to them. By optimizing a collection of convolutional deep networks with different hyperparameter (structural parameter) regimes and combining them, they showed that they can predict the average IT (and V4) responds reasonably well.

**Least Informative Dimensions**

Fabian Sinz, Anna Stockl, Jan Grewe, Jan Benda

Instead of maximizing mutual information between the features and target variable for dimensionality reduction, they propose to minimize the dependence between the non-feature space and the joint of target variable and feature space. As a dependence measure, they use HSIC (Hilbert-Schmidt independence criterion: squared distance between joint and the product of marginals embedded in the Hilbert space). The optimization problem is non-convex, and to determine the dimension of the feature space, a series of hypothesis testing is necessary.

**Dimensionality, dynamics and (de)synchronisation in the auditory cortex** (workshop)

Maneesh Sahani

Maneesh compared the underlying latent dynamical systems fit from synchronized state (drowsy/inattentive/urethane/ketamine/xylazine) and desyncrhonized state (awake/attentive/urethane+stimulus/fentany/medtomidine/midazolam). From the population response, he fit a 4 dimensional linear dynamical system, then transformed the dynamics matrix into a “true Schur form” such that 2 pairs of 2D dynamics could be visualized. He showed that the dynamics fit from either state were actually very similar.

**Sparse nonnegative deconvolution for compressive calcium imaging: algorithms and phase transitions** (main)

**Extracting information from calcium imaging data** (workshop)

Eftychios A. Pnevmatikakis, Liam Paninski

Eftychios have been developing various methods to infer spike trains from calcium image movies. He showed a compressive sensing framework for spiking activity can be inferred. A plausible implementation can use a digital micromirror device that can produce “random” binary patterns of pixels to project the activity.

**Andreas Tolias** (workshop talk)

Noise correlations in the brain are small (0.01 range; e.g., Renart et al. 2010). Anesthetized animals have higher firing rate and higher noise correlation (0.06 range). He showed how latent variable model (GPFA) can be used to decompose the noise correlation into that of the latent and the rest. Using 3D acousto-optical deflectors (AOD), he is observing 500 neurons simultaneously. He (and Dimitri Yatsenko) used latent-variable graphical lasso to enforce a sparse inverse covariance matrix, and found that the estimate is more accurate and very different from raw noise correlation estimates.

**Whole-brain functional imaging and motor learning in the larval zebrafish** (workshop)

Misha Ahrens

Using light-sheet microscopy, he imaged the calcium activity of 80,000 neurons simultaneously (~80% of all the neurons) at 1-2 Hz sampling frequency (Ahrens et al. 2013). From the big data while the fish was stimulated with visually, Jeremy Freeman and Misha analyzed the dynamics (with PCA) and orienting stimuli tuning, and make very cool 3D visualizations.

**Normative models and identification of nonlinear neural representations **(workshop)

Matthias Bethge

In the first half of his talk, Matthias talked about probabilistic models of natural images (Theis et al. 2012) which I didn’t understand very well. In the later half, he talked about an extension of the GQM (generalized quadratic model) called STM (spike-triggered mixture). The model is a GQM with quadratic term , if the spike-triggered and non-spike-triggered distributions are Gaussian with covariances and . When both distributions are allowed to be mixture-of-Gaussians, then it turns out the nonlinear function becomes a soft-max of quadratic terms making it an LNLN model. [code on github]

**Inferring neural population dynamics from multiple partial recordings of the same neural circuit**

Srini Turaga, Lars Buesing, Adam M. Packer, Henry Dalgleish, Noah Pettit, Michael Hausser, Jakob Macke

Under certain observability conditions, they stitch together partially overlapping neural recordings to recover the joint covariance matrix. We read this paper earlier in UT Austin computational neuroscience journal club.

## Machine Learning

**Estimating the Unseen: Improved Estimators for Entropy and other Properties**

Paul Valiant, Gregory Valiant

Using “Poissonization” of the fingerprint (a.k.a. Zipf plot, count histogram, pattern, hist-hist, collision statistics, etc.), they find a simplest distribution such that the expected fingerprint is close to the observed fingerprint. This is done by first splitting the histogram into “easy” part (many observations; more than square root # of observations) and “hard” part, then applying two linear programs to the hard part to optimize the (scaled) distance and support. The algorithm “UNSEEN” has a free parameter that controls the error tolerance. Their theorem states that the total variations is bounded by with only samples where n denotes the support size. The resulting estimate of the fingerprint can be used to estimate entropy, unseen probability mass, support, and total variations. (code in appendix)

**A simple example of Dirichlet process mixture inconsistency for the number of components
**Jeffrey W. Miller, Matthew T. Harrison

They already showed that the number of clusters inferred from DP mixture model is inconsistent (at ICERM workshop 2012, and last year’s NIPS workshop). In this paper they show theoretical examples, one of which says: If the true distribution is a normal distribution, then the probability that # of components inferred by DPM (with ) is 1 goes to zero, as a function of # of samples.

**A Kernel Test for Three-Variable Interactions
**Dino Sejdinovic, Arthur Gretton, Wicher Bergsma

To detect a 3-way interaction which has a ‘V’-structure, they made a kernelized version of the Lancaster interaction measure. Unfortunately, Lancaster interaction measure is incorrect for 4+ variables, and the correct version becomes very complicated very quickly.

**B-test: A Non-parametric, Low Variance Kernel Two-sample Test**

Wojciech Zaremba, Arthur Gretton, Matthew Blaschko

This work brings both test power and computational speed (Gretton et al. 2012) to MMD by using a blocked estimator, making it more practical.

**Robust Spatial Filtering with Beta Divergence
**Wojciech Samek, Duncan Blythe, Klaus-Robert Müller, Motoaki Kawanabe

Supervised dimensionality reduction technique. Connection between generalized eigenvalue problem and KL-divergence, generalization to beta-divergence to gain robustness to outlier in the data.

**Optimizing Instructional Policies**

Robert Lindsey, Michael Mozer, William J. Huggins, Harold Pashler

This paper presents a meta-active-learning problem where active learning is used to find the best policy to teach a system (e.g., human). This is related to curriculum learning, where examples are fed to the machine learning algorithm in a specially designed order (e.g., easy to hard). This gave me ideas to enhance Eleksius!

**Reconciling priors” & “priors” without prejudice?**

Remi Gribonval, Pierre Machart

This paper connects the Bayesian least squares (MMSE) estimation and MAP estimation under Gaussian likelihood. Their theorem shows that MMSE estimate with some prior is also a MAP estimate under some other prior (or equivalently, a regularized least squares).

There were many more interesting things, but I’m going to stop here! [EDIT: check out these blog posts by Paul Mineiro, hundalhh, Yisong Yue, Sebastien Bubeck, Davide Chicco]