scholarly journals Neural spiking for causal inference

2018 ◽  
Author(s):  
Benjamin James Lansdell ◽  
Konrad Paul Kording
Keyword(s):  
Membrane Potential ◽  
Causal Inference ◽  
Gradient Descent ◽  
Unbiased Estimate ◽  
Learning Problems ◽  
Causal Influence ◽  
Neural Spiking ◽  
Local Discontinuity

AbstractWhen a neuron is driven beyond its threshold it spikes, and the fact that it does not communicate its continuous membrane potential is usually seen as a computational liability. Here we show that this spiking mechanism allows neurons to produce an unbiased estimate of their causal influence, and a way of approximating gradient descent learning. Importantly, neither activity of upstream neurons, which act as confounders, nor downstream non-linearities bias the results. By introducing a local discontinuity with respect to their input drive, we show how spiking enables neurons to solve causal estimation and learning problems.

scholarly journals On the Convergence Properties of a K-step Averaging Stochastic Gradient Descent Algorithm for Nonconvex Optimization

2018 ◽  
Author(s):  
Fan Zhou ◽  
Guojing Cong
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Learning Problems ◽  
Stochastic Gradient Descent ◽  
Convergence Properties ◽  
Descent Algorithm ◽  
Convergence Results ◽  
Gradient Descent Algorithm ◽  
Parallel Stochastic Gradient Descent

We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG  for solving large scale machine learning problems. We establish the convergence results of K-AVG for nonconvex objectives. Our analysis of K-AVG applies to many existing variants of synchronous SGD.  We explain why the K-step delay is necessary and leads to better performance than traditional parallel stochastic gradient descent which is equivalent to K-AVG with $K=1$. We also show that K-AVG scales better with the number of learners than asynchronous stochastic gradient descent (ASGD). Another advantage of K-AVG over ASGD is that it allows larger stepsizes and facilitates faster convergence. On a cluster of $128$ GPUs, K-AVG is faster than ASGD implementations and achieves better accuracies and faster convergence for training with the CIFAR-10 dataset.

scholarly journals An Improved Gradient Descent Method for Optimization of Supervised Machine Learning Problems

2021 ◽  
Vol 183 (20) ◽  
pp. 39-45
Author(s):  
Dada Ibidapo Dare ◽  
Akinwale Adio Taofiki ◽  
Onashoga Adebukola S. ◽  
Osinuga Idowu A.
Keyword(s):  
Machine Learning ◽  
Gradient Descent ◽  
Descent Method ◽  
Supervised Machine Learning ◽  
Learning Problems ◽  
Gradient Descent Method

scholarly journals Stability and Generalization for Randomized Coordinate Descent

2021 ◽  
Author(s):  
Puyu Wang ◽  
Liang Wu ◽  
Yunwen Lei
Keyword(s):  
Machine Learning ◽  
Theoretical Analysis ◽  
Optimization Algorithm ◽  
Gradient Descent ◽  
Coordinate Descent ◽  
Learning Problems ◽  
Stochastic Gradient Descent ◽  
Strongly Convex ◽  
Generalization Bounds ◽  
Algorithmic Stability

Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to test examples. In this paper, we initialize the generalization analysis of RCD by leveraging the powerful tool of algorithmic stability. We establish argument stability bounds of RCD for both convex and strongly convex objectives, from which we develop optimal generalization bounds by showing how to early-stop the algorithm to tradeoff the estimation and optimization. Our analysis shows that RCD enjoys better stability as compared to stochastic gradient descent.

scholarly journals Stochastic Approximate Gradient Descent via the Langevin Algorithm

2020 ◽  
Vol 34 (04) ◽  
pp. 5428-5435
Author(s):  
Yixuan Qiu ◽  
Xiao Wang
Keyword(s):  
Expectation Maximization ◽  
Gradient Descent ◽  
Expectation Maximization Algorithm ◽  
General Purpose ◽  
Learning Problems ◽  
Stochastic Gradient Descent ◽  
Practical Implementation ◽  
Sampling Techniques ◽  
Tuning Parameters ◽  
Manual Intervention

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained. Traditional methods for such problems rely on general-purpose sampling techniques such as Markov chain Monte Carlo, which typically requires manual intervention for tuning parameters and does not work efficiently in practice. Instead, SAGD makes use of the Langevin algorithm to construct stochastic gradients that are biased in finite steps but accurate asymptotically, enabling us to theoretically establish the convergence guarantee for SAGD. Inspired by our theoretical analysis, we also provide useful guidelines for its practical implementation. Finally, we show that SAGD performs well experimentally in popular statistical and machine learning problems such as the expectation-maximization algorithm and the variational autoencoders.

scholarly journals Convergence Analysis of Gradient Descent for Eigenvector Computation

2018 ◽  
Author(s):  
Zhiqiang Xu ◽  
Xin Cao ◽  
Xin Gao
Keyword(s):  
Convergence Analysis ◽  
Gradient Descent ◽  
Symmetric Matrix ◽  
Linear Convergence ◽  
Learning Problems ◽  
Principal Angle ◽  
Global Rate ◽  
Convex Problem ◽  
Initial Iterate ◽  
The Given

We present a novel, simple and systematic convergence analysis of gradient descent for eigenvector computation. As a popular, practical, and provable approach to numerous machine learning problems, gradient descent has found successful applications to eigenvector computation as well. However, surprisingly, it lacks a thorough theoretical analysis for the underlying geodesically non-convex problem. In this work, the convergence of the gradient descent solver for the leading eigenvector computation is shown to be at a global rate O(min{ (lambda_1/Delta_p)^2 log(1/epsilon), 1/epsilon }), where Delta_p=lambda_p-lambda_p+1>0 represents the generalized positive eigengap and always exists without loss of generality with lambda_i being the i-th largest eigenvalue of the given real symmetric matrix and p being the multiplicity of lambda_1. The rate is linear at (lambda_1/Delta_p)^2 log(1/epsilon) if (lambda_1/Delta_p)^2=O(1), otherwise sub-linear at O(1/epsilon). We also show that the convergence only logarithmically instead of quadratically depends on the initial iterate. Particularly, this is the first time the linear convergence for the case that the conventionally considered eigengap Delta_1= lambda_1 - lambda_2=0 but the generalized eigengap Delta_p satisfies (lambda_1/Delta_p)^2=O(1), as well as the logarithmic dependence on the initial iterate are established for the gradient descent solver. We are also the first to leverage for analysis the log principal angle between the iterate and the space of globally optimal solutions. Theoretical properties are verified in experiments.

Two Timescale Analysis of the Alopex Algorithm for Optimization

2002 ◽  
Vol 14 (11) ◽  
pp. 2729-2750 ◽  
Author(s):  
P. S. Sastry ◽  
M. Magesh ◽  
K. P. Unnikrishnan
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Approximation ◽  
Approximation Method ◽  
Gradient Descent ◽  
Optimization Technique ◽  
Descent Method ◽  
Learning Problems ◽  
Gradient Descent Method ◽  
Gradient Information ◽  
Two Timescale Stochastic Approximation

Alopex is a correlation-based gradient-free optimization technique useful in many learning problems. However, there are no analytical results on the asymptotic behavior of this algorithm. This article presents a new version of Alopex that can be analyzed using techniques of two timescale stochastic approximation method. It is shown that the algorithm asymptotically behaves like a gradient-descent method, though it does not need (or estimate) any gradient information. It is also shown, through simulations, that the algorithm is quite effective.

Beyond metaphors and semantics: A framework for causal inference in neuroscience

2019 ◽  
Vol 42 ◽  
Author(s):  
Roberto A. Gulli
Keyword(s):  
Causal Inference ◽  
Causal Power

Abstract The long-enduring coding metaphor is deemed problematic because it imbues correlational evidence with causal power. In neuroscience, most research is correlational or conditionally correlational; this research, in aggregate, informs causal inference. Rather than prescribing semantics used in correlational studies, it would be useful for neuroscientists to focus on a constructive syntax to guide principled causal inference.

Measurement of spontaneous neuronal membrane activity by time lapse confocal microscopy

1995 ◽  
Vol 53 ◽  
pp. 972-973
Author(s):  
R H. Selinfreund ◽  
A. H. Cornell-Bell
Keyword(s):  
Membrane Potential ◽  
Confocal Microscopy ◽  
Patch Clamp ◽  
Electrical Activity ◽  
Time Lapse ◽  
Neuronal Firing ◽  
Neuronal Membrane ◽  
Pituitary Cells ◽  
Patch Clamp Recording ◽  
Spontaneous Electrical Activity

Cellular electrophysiological properties are normally monitored by standard patch clamp techniques . The combination of membrane potential dyes with time-lapse laser confocal microscopy provides a more direct, least destructive rapid method for monitoring changes in neuronal electrical activity. Using membrane potential dyes we found that spontaneous action potential firing can be detected using time-lapse confocal microscopy. Initially, patch clamp recording techniques were used to verify spontaneous electrical activity in GH4\C1 pituitary cells. It was found that serum depleted cells had reduced spontaneous electrical activity. Brief exposure to the serum derived growth factor, IGF-1, reconstituted electrical activity. We have examined the possibility of developing a rapid fluorescent assay to measure neuronal activity using membrane potential dyes. This neuronal regeneration assay has been adapted to run on a confocal microscope. Quantitative fluorescence is then used to measure a compounds ability to regenerate neuronal firing.The membrane potential dye di-8-ANEPPS was selected for these experiments. Di-8- ANEPPS is internalized slowly, has a high signal to noise ratio (40:1), has a linear fluorescent response to change in voltage.

Fluorescent potentiometric dyes for membrane-potential imaging

1994 ◽  
Vol 52 ◽  
pp. 166-167
Author(s):  
Leslie M. Loew
Keyword(s):  
Membrane Potential ◽  
Single Cells ◽  
Quantitative Imaging ◽  
Optical Recording ◽  
Biological Processes ◽  
Major Focus ◽  
The Past ◽  
Excitable Systems ◽  
Major Application ◽  
The Impact

A major application of potentiometric dyes has been the multisite optical recording of electrical activity in excitable systems. After being championed by L.B. Cohen and his colleagues for the past 20 years, the impact of this technology is rapidly being felt and is spreading to an increasing number of neuroscience laboratories. A second class of experiments involves using dyes to image membrane potential distributions in single cells by digital imaging microscopy - a major focus of this lab. These studies usually do not require the temporal resolution of multisite optical recording, being primarily focussed on slow cell biological processes, and therefore can achieve much higher spatial resolution. We have developed 2 methods for quantitative imaging of membrane potential. One method uses dual wavelength imaging of membrane-staining dyes and the other uses quantitative 3D imaging of a fluorescent lipophilic cation; the dyes used in each case were synthesized for this purpose in this laboratory.

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