The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation. The scale is staggering: over 1011 neurons, each making an average of 10 3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area. Slowly, we are beginning to acquire experimental tools that can gather the massive amounts of data needed to characterize this system. However, to understand and interpret these data will also require substantial strides in inferential and statistical techniques. This dissertation attempts to meet this need, extending and applying the modern tools of latent variable modeling to problems in neural data analysis. It is divided

The analysis of action potentials, or spikes, is central to systems neuroscience research. Spikes are typically identified from raw waveforms manually for off-line analysis or automatically by human-configured algorithms for on-line applications. The variability of manual spike sorting is studied and its implications for neural prostheses discussed. Waveforms were recorded using a micro-electrode array and were used to construct a statistically similar synthetic dataset. Results showed wide variability in the number of neurons and spikes detected in real data. Additionally, average error rates of 23% false positive and 30% false negative were found for synthetic data.

A traditional interpolation model is characterized by the choice of rcg- ularizcr applied to the intcrpolant, and the choice of noise model. Typi- cally, the rcgularizcr has a single rcgularization constant , and the noise model has a single parameter . The ratio / alone is responsible for de- termining globally all these attributes of the intcrpolant: its 'complexity', 'flexibility', 'smoothness', 'characteristic scale length', and 'characteristic amplitude'. We suggest that interpolation models should be able to cap- turc more than just one flavour of simplicity and complexity. Wc describe Bayesian models in which the intcrpolant has a smoothness that varies spatially. We emphasize the importance, in practical implementation, of the concept of 'conditional convexity' when designing models with many hyperparameters.

Abstract—This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution. Index Terms—Arrival time estimation, continuous wavelet transform, unsupervised spike detection. I.

Protein alignments are commonly characterized by the probability vectors over amino acids in each column of the alignment. This paper develops various models for the probability distribution of these probability vectors. First a simple Dirichlet distribution is used, then a mixture of Dirichlets. Finally a componential model employing a `density network' is described. These models are optimized and compared using Bayesian methods. 1

This paper deals with the problem of extracting the activity of indi-vidual neurons from multi-electrode recordings. Important aspects of this work are: 1) the sorting is done in two stages- a statistical model of the spikes from different cells is built and only then are occurrences of these spikes in the data detected by scanning through the original data, 2) the spike sorting is done in the frequency domain, 3) strict statistical tests are applied to determine if and how a spike should be classiffed, 4) the statistical model for detecting overlaping spike events is proposed, 5) slow dynamics of spike shapes are tracked during long experiments. Results from the application of these techniques to data collected from the escape response system of the American cockroach, Periplaneta americana, are presented.

Running Head: Spike Sorting based on Tuning Information. Current spike sorting methods focus on clustering the neurons characteristic spike waveforms. The resulting spike sorted data are typically used to estimate how neural inputs modulate the firing rates of neurons. However, when inputs do modulate the firing rates, they too provide information about spikes identities, which thus far has been ignored for the purpose of spike sorting. This paper describes a novel approach to spike sorting, which incorporates both waveform information and tuning information obtained from the modulation of firing rates by neural inputs. Because it is efficiently uses all the available information, this spike sorter yields lower spike misclassification rates than traditional automatic spike sorters. This theoretical result is verified empirically on several examples. The proposed method essentially consists of performing spike sorting and tuning estimation simultaneously rather than sequentially, as is currently done. It does not require additional assumptions; only its implementation is different, requiring a novel maximum likelihood algorithm. The resulting linked EM algorithm is the second main contribution of this paper. We present the general form of this algorithm and provide a detailed implementable version under the assumptions that neurons are independent and spike according to Poisson processes. Lastly, we uncover a serious flaw of spike sorting based on waveform information only.

We propose a new method of clustering neural spike waveforms for spike sorting. After detecting the spikes using a threshold detector, we use principal component analysis (PCA) to get the first few PCA components of the data. Clustering on these PCA components is achieved by maximizing the Cauchy Schwartz PDF divergence measure which uses the Parzen window method to non parametrically estimate the pdf of the clusters. Comparison with other clustering techniques in spike sorting like kmeans and Gaussian mixture elucidates the superiority of our method in terms of classification results and computational complexity. 1.

: 250, Introduction: 414, Discussion: 1493 Correspondence: Dr. Michael Lewicki The Salk Institute Computational Neurobiology Lab 10010 N. Torrey Pines Rd. La Jolla, CA 92037 Phone: 619-453-4100 x1124 Fax: 619-587-0417 E--mail: lewicki@salk.edu Acknowledgements: We thank Allison Doupe, Mark Konishi, James Mazer, and Marc Schmidt for valuable comments on the manuscript. This work was supported by a National Institute of Health Research Training Grant, a Caltech Engineering Research Center fellowship (MSL), and a National Science Foundation graduate fellowship (BJA). Lewicki and Arthur 1 Abstract Some of the most complex auditory neurons known are contained in the songbird forebrain nucleus HVc. These neurons are highly sensitive to auditory temporal context: they respond strongly to the bird's own song, but respond weakly or not at all when the sequence of the song syllables is altered. It is not known whether this property arises de novo in HVc or if it is relayed from the proper...

Spike sorting is of prime importance in neurophysiology and hence has received considerable attention. However, conventional methods suffer from the degradation of clustering results in the presence of high levels of noise contamination. This paper presents a scheme for taking advantage of automatic clustering and enhancing the feature extraction efficiency, especially for low-SNR spike data. The method employs linear discriminant analysis based on a fuzzy c-means (FCM) algorithm. Simulated spike data [1] were used as the test bed due to better a priori knowledge of the spike signals. Application to both high and low signal-to-noise ratio (SNR) data showed that the proposed method outperforms conventional principal-component analysis (PCA) and FCM algorithm. FCM failed to cluster spikes for low-SNR data. For two discriminative performance indices based on Fisher's discriminant criterion, the proposed approach was over 1.36 times the ratio of between- and within-class variation of PCA for spike data with SNR ranging from 1.5 to 4.5 dB. In conclusion, the proposed scheme is unsupervised and can enhance the performance of fuzzy c-means clustering in spike sorting with low-SNR data. Keywords: Spike sorting; spike classification; fuzzy c-means; principal-component analysis; linear discriminant analysis; low-SNR.