Online Neural Sequence Detection with Hierarchical Dirichlet Point Process
Authors: Weihan Li
Yu Qi
Gang Pan
Venue: NeurIPS 2022 Accept (2022)
Keywords: Neural sequence detection
Online learning
Dirichlet process mixture model

Abstract: Neural sequence detection plays a vital role in neuroscience research. Recent impressive works utilize convolutive nonnegative matrix factorization and Neyman-Scott process to solve this problem. However, they still face two limitations. Firstly, they accommodate the entire dataset into memory and perform iterative updates of multiple passes, which can be inefficient when the dataset is large or grows frequently. Secondly, they rely on the prior knowledge of the number of sequence types, which can be impractical with data when the future situation is unknown. To tackle these limitations, we propose a hierarchical Dirichlet point process model for efficient neural sequence detection. Instead of computing the entire data, our model can sequentially detect sequences in an online unsupervised manner with Particle filters. Besides, the Dirichlet prior enables our model to automatically introduce new sequence types on the fly as needed, thus avoiding specifying the number of types in advance. We manifest these advantages on synthetic data and neural recordings from songbird higher vocal center and rodent hippocampus.

Online Neural Sequence Detection with Hierarchical Dirichlet Point Process
Weihan Li Yu Qi2.3,+, Gang Pan
"College of Computer Science and Technology, Zhejiang University, Hangzhou, China The Affiliated Mental Health Center & Hangzhou Seventh People's Hospital, the MOE Frontier Science Center for Brain Science and Brain-machine Integration, Zhejiang University School of Medicine, Hangzhou, China Intelligence, Zhejiang University, Hangzhou, China
The State Key Lab of weihanli0p izzju. edu..edu.coo cn, qiyu@zju. edu. cn, gpanšzju edu. cn
Abstract
Neural sequence detection plays vital role in neuroscience research. Recent impressive works utilize convolutive nonnegative matrix factorization and Neyman- Scott process solve this problem. However, they still face two limitations. Firstly, they accommodate the entire dataset into memory and perform iterative updates of multiple passes, which be inefficient when the dataset large grows frequently. Secondly, they rely on the prior knowledge of the number of sequence types, which can be impractical with data when the future situation is unknown. To tackle these limitations, we propose a hierarchical Dirichlet point process model for efficient neural sequence detection. Instead of computing the entire data, our model can sequentially detect sequences in an online unsupervised manner with Particle filters. Besides, the Dirichlet prior enables our model automatically introduce new sequence types on the fly needed, thus avoiding specifying the number of types in advance. We manifest these advantages on synthetic data and neural recordings from songbird higher vocal center and rodent hippocampus.
Introduction
Neural sequences are a set of sequential firing neurons repeatedly occurring over time, and they play crucial roles in understanding the brain activities of working memory 100, motor production [9]. and memory replay 44. However, in general, it's hard directly observe neural sequences from high-dimensional neural recordings due to the unsorted neurons. Besides, methods that use linear dimensionality reduction neural populations may be inappropriate to handle such sequences since they form high-dimensional structure and cannot be efficiently summarized by low-dimensional representation [15] 23). Finally, the relationship between neural sequences and behavior is not always so regular and predictable 30 Thus an unsupervised method to identify neural sequences is required.
While recent works [15
have made great process neural sequence detection, they have two drawbacks when it comes to the contexts of online learning. Firstly, they are ill-suited to accommodate new data or handle large datasets. Many real-world neural recordings involve many hours' or days' signals that sometimes may be hard to accommodate entirely in the memory. Furthermore, the inference algorithms of these works (e.g., coordinate descent, Gibbs sampling, etc.) maintain the entire data and perform iterative updates of multiple passes, which may be a waste of both computational and storage resources. Secondly, these works require the number of sequence types to be specified in advance, which is inappropriate when future situation is unknown.
20 28
Corresponding authors: Yu Qi and Gang Pan
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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To address these problems, we propose a hierarchical Dirichlet point process (HDPP) with an efficient online inference algorithm. Briefly, we use a two-level structure in our approach. At a lower level, we model the set of neural sequences by a Dirichlet nonhomogeneous Poisson process: The observed spikes are considered as a mixture of neural sequences, and those spikes belonging to different sequences are modeled via different nonhomogeneous Poisson processes, for which the intensity of each process varies across neurons and times. At a higher level, we model the types of sequences by Dirichlet Hawkes process [5:: The detected sequences are partitioned into an automatically inferred number of types. The temporal dynamics these sequences are captured by several Hawkes processes [II, where each process's 's distinctive temporal relation will help our model to disambiguate different types of sequences with spatial overlapping neurons. Besides, the prior of each sequence type is given by Dirichlet distribution, so either the number of sequences or sequence types could vary during inference. Note that our model has only one Dirichlet point process at the lower level, which differs from the classical hierarchical Dirichlet process (HDP) 25
We derive a Particle filter 2
22 to learn the HDPP in an online manner: (1) learn the model with single pass of the data; (2) make the decisions regularly without requiring future data M. In particular, we use a collection of particles to sequentially approximate the posterior, taking in one spike at time to make the update. We also develop specific mechanisms to merge similar sequences and prune inaccurate ones during inference, thus further improving the performance. We evaluate the proposed model synthetic data as well as real- real-world data from songbird higher vocal center [I5] and rodent hippocampus 3 7 8] Results show the proposed model can properly identify the neural sequences and be robust to noise in single pass over the data.
The contributions of our work include: (1) We propose a novel hierarchical Dirichlet Point Process
for neural sequence detection, and different from prior works [14 (8) our model does not specify
the number of sequence type in advance, while determines adaptively during inference. (2) Our
model with efficient online inference algorithm performs comparably to the state-of-the-art (28
with significantly lower time cost. (3) We use a group of Hawkes processes to capture the temporal dynamics of different types of sequences, which enables our model to distinguish sequences with spatial overlapping neurons.
2
Related works
Previous studies about neural sequence detection can be divided into three classes: supervised, bottom-up unsupervised, and top-down unsupervised (32]
Supervised methods. Averaging spikes times over multiple trials is the simplest and most used supervised method to identify neural sequences. This approach requires simultancous sensory cues or behavioral actions recording and uses a template matching procedure to discover exact timestamps of each sequence 222 18] [9]. However, as previously mentioned, the relationship between neural activity and behavior is not always reliable (30.. Thus this approach may be useless under certain circumstances.
Bottom-up unsupervised methods. Bottom-up unsupervised methods 23 24 26
usually identify
neural sequences via variety of statistics between pairs of neurons (e.g., corsssosrrsssioons.. These methods may be beneficial when involving small numbers of neurons [32] but they have high computational complexity and low statistical power when dealing with a large number of neurons.
Top-down unsupervised methods. Top-down unsupervised methods can be detined as kind of method that discovers a sequence from the perspective of the whole population and is robust to noise the level of individual neurons [32] Maboudi al. 14 identifies neural sequences by visualizing the transition matrix of Hidden Markov Models. Peter et al. 200 and Mackevicius et al. [15 use convolutive nonnegative matrix factorization (ConyNMF) with different regularizations to factorize the neural data into couple of neural factors and temporal factors, where each neural factor encodes a type of neural sequence and each temporal factor indicates the times of sequences. Williams et al. Neyman-Scott process (PP-Seq), a spatial-temporal point process
28 models neural sequences originally designed to discover clusters in the galaxy. Each sequence in this model corresponds to a latent cause that generates spikes as the offspring events.s

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Background
A basic probabilisticc model of continuous-tinn time stream is temporal point process whose re- alization can be represented as an event sequences {r;} = {tz t2....} with times of occurrence [0, T]. A way to characterize temporal point processes is via intensity function X(t), for which (()) equats the expected instantaneous rate of happening next event given the history. The functional form of X(t) varies among different phenomena of interest. In homogeneous Poisson process (PP), X(t is assumed to be a constant over time, while in a nonhomogeneous Poisson process, X(t) is time-varying and independent of the history.
Hawkes process. A Hawkes process (HP) III is a self-exciting nonhomogeneous Poisson process in which past events in history have influenced the intensity of current and future events. Such influences are positive but decay exponentially with time:
(tt) Ao + + Eexp( 5(t t,)),
where Ag is the base intensity independent of the history, a is the kernel parameter, and ō is the decay rate of that influence. An important extension of the Hawkes process is to incorporate additional information about each event, for example, an associated event "label" ky with each event v; = (44, k:). As consequence,
define Hawkes process as sum of independent Hawkes processes from different types based on the superposition principle: A(t) Σ (t), where (x(t) is the intensity function from k-th category.
Dirichlet Hawkes process. Dirichlet Hawkes process (DHP) 5 16 is method naturally handle infinite mixture clusters with temporal dependency. As opposed to traditional parametric models, DHP allows the number of clusters vary over time. It uses Hawkes process model the intensity of events (e.g.. the times of neural sequences), while the Dirichlet process captures the diversity of event types (e.g.. the clusters of neural sequences). Similar the Dirichlet process, DHP, typically denoted by (Ao, 0) is characterized by a concentration parameter À and a base distribution It uses the samples 01:K from base distribution 0 and collection of triggering kernel functions do, (t, 14) the parameters for modeling K different event types. Then, the events (t;, 6,) from DHP(>g, 0) can be simulated as follows:
1. Sample from PP()o) and 0₂ from 0.
2. For n > 1, sample in from HP(Ao + Σ An((n)
Sample a new 0K+1 from 0 with probability: Ao/(Ao + Ek Ab(tn))
Reuse previous 0₂ with probability: Au(4n)/(Ao =K (n()n)
where (t,)) = -En= 9e, (tn, I,) = 0x) is the intensity function of a Hawkes process for past events with type
4 Hierarchical Dirichlet Point Process of Neural Sequences
We model the neural sequences as hierarchical Dirichlet point process (HDPP). We use Dirichlet nonhomogencous Poisson process as the prior for observed spikes while using a Dirichlet Hawkes process as the prior for neural sequences. As in Figure 1, the goal of HDPP is to sequentially identify sequences from observed spikes, then partition these sequences into different types based on both temporal dynamics and included neurons.
Consider a continuous-time spike train data with N neurons, its observed spikes can be denoted by set of S labeled events I, = nt, n,, k2) referring to the spike time, t, E [0, T). neuron, ns E {1...., N) and indicator to the sequence that x, belongs to, ke E [I,..., K). Note that the indicator k, remains unknown until we infer the sequences from the data. Similarly, the inferred neural sequences can also be represented as a collection of tuples ga = m)) referring to the time Tk [0, I'll and indicator for sequence type my E M.
3

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(r, 11)
4;- 22 9,- m -1)
Neunon
Temporal dynamics of sequences
Spikes with
annotated
Raw spikes
Nearow
Three detected
Figure A case with K sequences and M = 2 types of sequences is shown. The proposed model considers observed spikes mixture of neural sequences, where the spikes of different neurons within a sequence can be modeled via a nonhomogeneous Poisson process that catches their firing rates. Likewise, the detected sequences also mixture of certain types of sequences, where their temporal dynamics are captured by several Hawkes processes.
According to the definition of the Dirichlet Hawkes process, for spike x, occurring at time 4, its probability of belonging to the k-th neural sequence is:
(tx)
P(k, klt,)
9o
Jnuise Ek=1gk(t,)
where go is the concentration parameter, Inoise is the firing rate for background spikes, and (t(() is the intensity function of sequence 9k, controlling the temporal dynamics of related spikes. Likewise, sequence is given by:
the probability of assigning spike 2g either background noise
Sheiee P(k, k((()) Groise EK ax (ta)
for k 0,
9a
for K + 1.
E 2 (t.).
After neural sequence ORso is chosen, we assign it to existing type create new type the fly as needed with probability:
Am S
for E (1,..,,M,,
P(m+ = mlTx)
Ao + 2ma-1 Am
Am(TT))
(4)
M 1.
Ao Σ Am (Tk)
where (m( is the intensity function that captures temporal dynamics of sequences in type Note that we assume Ok (t) and (T) take different functional forms, and gkn (t) can be viewed as the firing rate of neuron caused by sequence 9k- Following the work in 288 represent yen (t) via Gaussian form as:
(5) Here Om Mmme and Omg n parameters of each sequence type my, indicating the weight, offset, and width of neuron nt's firing rate. 3g the amplitude of sequence Qe. denoting the expected number
gknn (t) Omgnn 3r (N + Amgns my mmpn).
of spikes induced by qe (28). For Am()), opt the similar form (I). with parameter am 0 controlling the self-excitation of previous sequences, hyperparameter ó > controls the decay and hyperparameter 77 denotes the expected time interval of sequences:
Am
Olm Σ exp( exp(-5((= - тk - [O) = 0m))
(6)
Th
Based on the definition of (t)()) and Ar), we regard that the temporal dynamics of spikes and neural sequences are captured by nonhomogeneous Poisson process and a self-exciting Hawkes process, respectively. For sequence type parameters am. {8 J.y and {(mm: mmn) N we assume they follow Gamma distribution, a Dirichlet distribution, and normal-inverse-d uuraa--i distribution 17 28 for every neuron and type. For amplitude 3g and background spike rate fnoises we assume they obey a Gamma distribution. Then, we can describe the proposed hierarchical Dirichlet point process in generative way as:

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1. For neural sequence Gc. HP(AO - Em=i (m( Pp ~ Gamma(a3 (01. b1).
2. Sample sequence type my using 4
If my = M 1: M+ Dir(Ou), (#M+1,0M++)) ( No, uo, Go), aM++1 Gamma(az, b2) and M M +.
3. Sample spikes induced by sequence qs: Sk= = Poisson(SE). {ng]am ~ Categorical and { ~ ~N(T== Mmnnn Omgn,)
4. Sample background spikes during time interval At = Th 7k-12 Jnvise ~ Gamma(ao bo),
Sg Poisson( (noise
At), {n) Categorical (Onoise) and {ts]am Uniform((T=-1.71I]
where 8n is hyperparameter parameter for Dirichlet prior, ag by, d1, b1, 022 b2 are hyperparameter parameters for Gamma prior, and μuu Ku, Ub dg are hyperparameter parameters for chi-squared prior.
5 Inference
Given spikes fx,- (ts. n,,)),,)111. as previously discussed, the model aims to sample neural sequences use set of particles to sequentially approximate
indicator k for each spike. Using this insight, posterior P(kizal4 R1:.), while sampling indicator m. for each sequence.
We derive Particle filter approach for our proposed model. This inference algorithm exploits the temporal dependencies in the observed spikes to sequentially sample the latent variables. To efficiently sample from the posterior distribution, Particle filter keeps track of an approximation of P(k)a-11fi:--1, 71:s-1), and updates it to have an approximation for P(k (tie, N1:a) when receiving newly observed spike. The approximation is evaluated by set of weighted particles {p)?, where the weight of each particle reflects how well the observed spikes are explained.
For each particle p, its weight is defined as the ratio between true posterior and importance distribution:
w ((:k,,/ ((ka=eltss,,1:2)) As the work in [ 3 did, choose P(k,) (1kg//1:s-11 1, 11ss, N1:s) be the importance distribution. Next, the unnormalized weight w can be updated as:
w x w²11" P(n,, k "1:s-1)-
Here, let C \r, Ca,,, \a, denote the spike counts of sequence type my, and spike counts of neuron ny in sequence type m,,, both excluding xs. The likelihood P(n, |Kis> R1:8-1) is given by Dirichlet- Categr-catl conjugate relation [6]
C mks A + Oon,
CUm, Ye, + Σ n= Oon
After sampling indicator k, from posterior P(ka 2,, f2,, rest) for each spike, then sample the type indicators my from posterior P(mulTi , Xk, rest). The posteriors of both indicators are determined by the likelihood of the spike/sequence assigned to given sequence/sequence type and by the temporal prior under Dirichlet nonhomogeneous Poisson process ( or Dirichlet Hawkes process
P(ka, [a, ns rest) x P(nglkis
P(mm/ Ik; XR. rest) P(Xg|me, rest) Pmmm [Ts, rest),
(10)
where rest represents all other latent variables with T1:s-1, X₂ = (n, h2 = k} is the neurons in k-th sequence. The exact form of the two posteriors is given in Supplement A.
Updating parameters. There are three groups of parameters that need to be updated after attributing each spike to neural sequence: sequence type parameters O,,, (0... Omm {pmn J.N {a J. sequence parameters θ₁ = {Tk. 3% and background parameters Oş = Juoise Following the literature in Particle filter devoted the estimation of an online parameter 2]. for most parameters, perform a single Gibbs sampling step to sample from their closed-form posterior under conjugate relation. Details about derivations in Supplement B.
Merge and Prune. Generally speaking, neural sequences created during this sequential inferring procedure often truly needed, as the decisions add new sequences are based on the accumulated
5

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knowledge from the past. However, there is still chance that some sequences generated at early samples would become incorrect and that multiple sequences may be close time. Thus, introduce a mechanism to merge similar sequences and prune incorrect ones.
The similarity of two sequences Qk and O3' be defined in terms of the time difference between Th and Tx', as d(ki kk) = Th - Tgl We will merge sequences qex qE' and their associated sufficient statistics when d(k, k)) < Aa. We also check the variance of firing times for each neuron in every sequence. That is, we reserve the spikes which fire consecutively in the same neuron n: Var( (=m)))))))m)))))))))))))))))))) < while removing those that appear to be sparsely distributed. Besides, we will remove an entire sequence if it has too few spikes after pruning. Note that there no need perform a such merge or prune at every iteration. Since the operation of merge sequences takes O(K) and computing variance for each sequence takes ((s,, NN). we propose examine similarity and variance at fixed interval Oii T) and only for the current sampled sequence.
The overall pseudocode for inference is presented in Algorithm D and its time complexity is O + M)), where S is the number of spikes, P is the number of particles, K' is the number of sequences, and M is the number of types. Our code is available at https: t/gttbbb//uu...... thub. com/
Algorithm 1: Particle filter for HDPP
Input: Spikes {ar, (lx, n,))
) ) hyperparameters and threshold e. Initialize particle weight wp to p for all p (1,.., P):
for each spike (t,,, fg nz), 1,.., S.....e do
for p E f1..., P} do
Sample sequence indicator k, from 9
Sample sequence type indicator my from (10):
Update the parameters O.. Ox and Og:
Update the particle weight by 7
end
Normalize particle weight; || < e then
2
Resample particles
end end
Experiments
6.1 Synthetic Data
We created three kinds of synthetic data to investigate the robustness to noise, the effectiveness of temporal dynamics, and the ability to infer the number of types of sequences, respectively, of HDPP: (1) Two types of sequences with background noise. (2) Two types of sequences occur side-by-side with spatial overlapping neurons. (3) A large set of sequence types with spatial overlapping neurons, where they are much uncertainty in sequence types.
Robustness to background noise. Figure 2(a) presents the first case of synthetic data, which demonstrates the robustness HDPP. This data has N = 60 neurons and = 30 spikes (Figure 2(a) left panel) show visible neural sequences. However, sequences are revealed by sorting the neurons with the learned weight, type, and offset of this sequence. Besides, background spikes can also be correctly identified as noise.
=0 seconds. The raw
Distinguishing overlapping sequences. Figure 2(b) shows much more complex case where two sequences with overlap populations of neurons occur side-by sidebb--idde. This data has N = 60 neurons and 20 seconds. Usually, it's hard to distinguish these sequences from the perspective of neurons. But with the help of temporal dynamics, HDPP could be able to capture sequences' distinctive intensity functions (Figure 2(b) top panel), and disambiguate them to different types. Note that the intensities at the very beginning are missing since HDPP resamples type indicator for the first

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White Mivil
HERP Consleas
Murrn
undar RDC
Time
15
30
Time
HOPP: Infor the typss sequences from data
PP-Seq: Infer types sequences through
A Dirichiet prior with categories
A Dirichiet prior with 11 categories
Neurona
Time
Figure 2: Synthetic data. (a) Two types of sequences with background noise. Raw spikes (left), neurons re-sorted by HDPP (middle), sequences annotated by HDPP (right), and corresponding intensities captured by Hawkes processes (top). (b) Two types of highly overlapping sequences occur side-by- side-by-side with background noise. (c) Comparison of HDPP and PP-Seq on large set of sequence types with spatial overlapping neurons. HDPP can infer the types of sequences from data (d) Comparison of HDPP, PP-Seq, and convNMF identify sequences under different levels of background noise. HDPP is robust to background noise.
sequence whenever it receives spike and those empty types dropped as well as their recorded intensities.
Inferring the types of sequences from data. Figure 2(c) shows the comparison of HDPP and PP-Seq, demonstrating that HDPP can infer the number of types from data. This data has N 60 neurons and T = 400 seconds, where there are 11 different types of sequences: 6 types of smaller sequences involving 10 neurons, while other 5 types of larger sequences involving 20 neurons. Note that the larger sequences and smaller sequences have spatial overlapping neurons. HDPP could be able to distinguish the sequences with overlapping neurons without prior information on the number of types (Figure 2(c), left panel), while PP-Seq identifies the larger sequences setting the prior of types to a Dirichlet prior with 11 categories (Figure 2(c), right panel).
type when
Further, we also tested the robustness of HDPP quantitatively with the area under receiver operating characteristic (ROC) curves as metric. To keep line with previous work [28] we simulated dataset with M = sequence type and N = 100 neurons, where we varied the background spikes Inoise to quantitatively measure the robustness. From the results of the area under ROC Figure 2(d), HDPP achieves promising results we increase the noise levels.
6.2
Performance with Neural Recordings
6.2.1 Songbird Higher Vocal Center Recording
For real-world data, we first applied our model to the deconvolved spike train from functional imaging data recorded in songbird HVC during singing [15 One of the core features of this data is the high variability of the song, thus making it difficult to identify neural sequences by template-matee matching procedure.
Identifying neural sequences from Songbird Recording, Figure 3(a) visualizes the results from HDPP and Pe where we chose the neurons whose weight [fmp] NN was above a threshold, and sorted them based on each sequence's type my and offset {pma)er Figure 3(b)-(c) visualize
httt:///gttaab.cc/////LLLaa////p
httpp:///gthabbbooo//mneemmmaaa

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(4)
Raw Spikes
Offect
HDPP
(6
Naurona
Traking Testing
Sequance Type?
Log Laodeehh
Type2
2
HDPP
PP-5at
Figure 3: Songbird Higher Vocal Center data. (a) Raw spike train (left) and comparison of detected sequences by HDPP (bottom) and PP-Seq (top). (b)(c) Visualization of learned offsets and weights for sequence type (blue) and sequence type 2 (red). (d) The number of detected sequences over five independent runs. (e) The log-iikllhooos comparison of HDPP and PP-Seq.
the learned offset and weight from HDPP. For offset {Ama 1 there is a clear time-shift among different neurons (+ 0.25s for type 1 and + 0.3s for type 2), and for weight {m \/v the two sequence types have their own preference for neurons (neuron 27-62 for type and neuron 1-26 for type 2). Figure 3(d) indicates HDPP converges to similar parameter ranges: The total number of detected sequences over five independent runs (different random seeds for initiation) are close to each other. Finally, Figure 3(e) shows the log-likelihood comparison HDPP and PP-Seq averaging over different runs.
6.2.2 Rodent Hippocampal Recording
We then tested our model on more complex spike train data from a rat's hippocampal recording
when it performs repeating runs down wooden 1 1.6m linear track 3 8 7 The session we used is " "Achilles 10252013", which has N 120 neurons and T 2068 seconds. As (8), we expect to observe two sequences encoding the two opposite running directions on this liner track. To have good knowledge of hyperparameter settings, we performed cross-validation via "speckled holdout pattern" strategy, which was previously used in PCA (33,, and has recently been applied to neural data [28] [2]. We then evaluated the performance of HDPP by calculating log-likellnn ligliikll on the held-out set.
Identifying neural sequences from Hippocampal Recording, Figure 4(a)-(c) shows the raw spikes, sorted results, and two types of sequences annotated by HDPP, where we can clearly observe two groups of place coding neurons revealed by the sequences. Figure 4(d) presents the validation log-likelihoods of four key hyperparameters in HDPP, while other parameters have less impact on performance or are easy to locate the optimal range. For the sequence amplitude 3R, we randomized the mean sequence amplitude d1 and set the variance of sequence amplitude 4 equals to the mean.
For the background noise amplitude, we randomized the prior rate by in gamma distribution and set the prior shape dg to 100. According the results, HDPP on this data prefers larger sequence amplitude 3д (higher mean sequence amplitude by ), higher width dg the NIx² distribution, lower noise firing rate Inoise (lower mean noise firing rate (e), and higher concentration parameter go in the Dirichlet nonhomogeneous Poisson process.
6.3 Scalability to Large Dataset
To scale with large recordings, HDPP is supposed to process each spike in an expected constant time. In other words, the time cost of either calculating intensity functions or updating parameters should not grow with the number of sequences detected. In HDPP, we can note that the influences of past sequences decay exponentially. Using this insight, we can reduce the computational load by ignoring those past sequences far away from the current time. More specifically, given time window At, we
http://crens. bogg/ata--aae sets/hc/hc-11

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(b)
(c)
(d)
Validation
Validation
Validettio
Validaation
4.-
34
sequence amplltude
firing
firing
parameter
(e)
minutess
HDPP
HDPP
Paratel PP-6ig
Parallet PP
Secondde per 3000 spikes
Parallal PP-Gea Langtt 58
Longth
04
10
15
100
Dataset minutes
number Detected
Figure 4: Rodent hippocampal recording. (a) Raw spike train (T ~ 4.6 minutes is shown). (b)
Neurons sorted by HDPP. (c) Two types of sequences identified by HDPP. (d) The validation log-likelshoods on four key hyperparameters. Each boxplot involves five different values of hyperparameter, while other hyperparameters are set fixed values. (e) Performance comparison between HDPP and parallel PP-Seq on rodent hippocampal recording. (f) HDPP's time cost as function of detected sequences.
maintain active list of sequences ]K where Th At. Similarly, using temporal windows is also acceptable for PP-Seq by limiting the max length of each sequence, which is supposed to reduce loop operations. The test of performance was carried by desktop with AMD Ryzen 5800X 8-Core Processor and 32 GB RAM. Figure 4(c) shows the performance comparison between HDPP and PP-Seq on rodent hippocampal recording. For HDPP, we set the particle number to 20, and for PP-Seq. we adopt parallel MCMC to parallelize the computation well as setting the number of Gibbs sweeps to 2100 (28) The results indicate that HDPP still faster than parallel PP-Seq though it benefits from the temporal window. Figure 4(f) presents the time cost as function of detected sequences, which empirically verifies that HDPP has a constant time cost per spike after settling in.
7 Discussion
We present a hierarchical Dirichlet point process (HDPP) for neural sequence detection with an efficient online inference algorithm. The proposed model follows the framework the Dirichlet process, where the spike firing rates of sequence are modeled process, and the temporal dynamic of this sequence is captured via a Hawkes process. Unlike previous works, HDPP learns the number of sequence types adaptively during inference and takes in data in a streaming fashion, thus can be easily adapted to new data or large neural recordings. In the experiments, favorable results from both synthetic data and real-worle spike recordings have demonstrated that HDPP can reliably and efficiently identify neural sequences in a single pass.
nonhomogeneous Poisson
However, our model may fail in some conditions: (1) Time warping noise. Our model does not model the variability in sequence, which common phenomenon in neural data 28 28 3T. (2) A Low firing rate of neurons. Generally speaking, a high firing rate makes identifying sequences from background

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noise easier. As the firing rate becomes lower, our model's and existing methods' performance decreases (supplement material Figure 1). Furthermore, is an exciting future direction to investigate how we can learn HDPP via online variational inference without truncated approximation of the stick-breaking construction 13 27
Acknowledgements
This work partly supported by grants from the China Brain Project (20212D0200400), and Natural Science Foundation of China (U1909202, 61906166, 61 61925603), and the Key Research and Development Program of Zhejiang Province in China (2020C03004).
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
(c) Did you discuss any potential negative societal impacts of your work? [Yes]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes]
(b) Did you include complete proofs of all theoretical results? [Yes]
3. If you experiments..
(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either the supplemental material or as URL)? [Yes]
(b) Did you specify all the training details (e.g., data splits. hyperparameters, how they were chosen)? [Yes]
(c) Did you report error bars (e.g.. with respect the random seed after running experi- ments multiple times)? [Yes]
(d) Did you include the total amount of compute and the type of resources used (c.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes]
(b) Did you mention the license of the assets? [Yes]
(c) Did you include any new assets either in the supplemental material or as a URL? [Yes]
(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating? [Yes]
(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [Yes]
5. If you used crowdsourcing or conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, applicable? [N/A]
(b) Did you describe any potential participant risks, with links Institutional Review Board (IRB) approvals, if applicable? [N/A]
(c) Did you include the estimated hourly swage paid to participants and the total amount spent on participant compensation? [N/A]
12


Reviews:
[{"review_id": "fm-gIlBZ8TQ", "reviewer": "Reviewer_Pow4", "summary": "This paper proposed a neural sequence detection method, which is based on a so called ''hierarchical Dirichlet point process''. The model can jointly infer an unbounded number of sequences and the event types from data. The paper develops an online algorithm to process the neural spike data, with the particle filtering framework. The proposed method was evaluated on two real-world datasets. ", "questions": "see above", "limitations": "N/A", "rating": 3, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The application is very interesting and important\n2. The experimental data is interesting. From the test log-likelihood, the proposed algorithm seems working. \n\nWeakness: In summary, there is a big issue in the presentation and the contributions seem weak. \n1. The problem formulation is not clear. A good paper should give a clear definition and motivation of the problem you want to solve, but i did not see it in this paper, making me very confused.  Why do you want to partition the neural spikes into sequences? What is the meaning of doing so?  Aren't the observed events already a sequence by time? For a new sequence (inferred by the model), based on what the events are ordered? The notations confuse me further --- according to line 118, on the spike-train data, you've already had k_s to indicate the neural sequence, why do you want to infer them again with the model (see Eq2)? \n\n2. The relationship with the classical HDP is not mentioned. The name is confusing in that I thought you are building a model similar to  the HDP of (Teh et. al. 2005). However, it is not. The classical HDP uses the first-level DP to sample an infinite set of bases, and each DP in the second level will share these bases, but generate the data with different mixture weights. It took me a while to find out that this paper is not following the HDP framework. Rather, it is more like a hybrid of two DPs, one is to partition the data into sequences, and the other to partition the events into types. I do not see a clear ``hierarchical'' structure here. The paper should highlight the difference with the classical HDP, to avoid unnecessary misunderstanding. \n\n2. The contributions seem weak. The proposed model is  an extension of Dirichlet Hawkes process by (Du et. al., 2015). One more DP is added, and it is quite incremental. The inference, based on the particle filtering, is almost the same as the SMC used by (Du et. al., 2015), plus some heuristics to merge and prune. If there are some more significant contributions, the authors should highlight them. Otherwise, I view this is a very incremental extension of   (Du et. al., 2015), applied to spike-train data analysis. \n\n3. The quantitative metric is only based on test log-likelihood. I have a lot of experience of doing point process modeling. Although many works use test log-likelihood for evaluation, it is not a reliable metric, and is quite misleading. I look forward to seeing some evaluation that can truly reflect the performance, such as future event time prediction. ", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}, {"review_id": "fEu130Htzv_", "reviewer": "Reviewer_dbDh", "summary": "This paper proposes an unsupervised learning approach to detect and cluster neural spike sequences in neural spike data. To model the data, the authors propose a hierarchical Dirichlet point process model, which employs Hawkes processes to model the temporal dynamics of neural activity within sequences, whereas spike rates within a sequence are modelled via a non-homogeneous Poisson process. The authors derive a particle filter based online inference method to detect sequences and infer their types. They use conjugate priors to derive closed-form updates for obtaining posterior distributions of model parameters. The authors evaluate the performance of their method on both synthetic and real datasets.", "questions": "- Have you considered or run experiments where you analysed the convergence behaviour of your methodology by assessing how often you manage to recover ground-truth parameters if you optimise on data generated by the process described in section 4, lines  145-152?\n\n- Why have you not compared PP-seq across the board? How does PP-seq's likelihood compare with the likelihood of your approach?\n\n- Can you elaborate what do you compute ROC curves on in section 6.1? Why to you use just one type of sequence for the experiment?\n\n- How does your method perform if there is a greater (spatial and/or temporal) overlap between sequences than what we can see in synthetic datasets?", "limitations": "I have highlighted technical limitations and weaknesses above. I have nothing further to add here.", "rating": 7, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The authors propose a well-grounded probabilistic generative model for modelling neural activity sequences in spike train data\n- The model is able to infer the number and types of sequences from the data \n- The authors have devised a tailored particle filter to infer unobserved latent variables for identifying neural activity sequences and inferring their types, which in turn allows for closed-form updates of posterior distributions over model parameters \n- The results on artificial data indicate that the proposed methodology can detect and correctly identify the types of underlying neural sequence activity in the presence of background noise. \n- The results on real data are qualitatively interesting and comparable to the results of another approach. \n- The proposed methodology in principle is scalable to larger datasets with up to 210k spikes.\n\nWeaknesses:\n- No analysis is done to show how often the inference procedure leads to suboptimal solutions, which requires reruns of measures like merging and pruning as highlighted by the authors. \n- Experiments on synthetic data involve very low number of sequence types (up to 3), so it is hard to see how the (inference) method would perform for a larger number of sequence types  \n- Comparison with the alternative approach was only done on one data set. \n\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "SV2HmJ1T74", "reviewer": "Reviewer_hJrD", "summary": "The authors propose a hierarchical, non-parametric Bayesian model to identify neural sequences from neural spike data and then to categorize the neural sequences, all in an online manner. Specifically, their model consists of a Dirichlet nonhomogeneous Poisson process (DPP) prior for observed spikes and a Dirichlet Hawkes process (DHP) prior for the neural sequences generating those observed spikes. They refer to their model as the Hierarchical Dirichlet Point model (HDPP). They present a particle filtering method to perform inference under their model as well as a scheme for merging and pruning neural sequence categories/types that may have been incorrectly generated early during inference. They compare their method to two other top-down unsupervised methods, ConvNMF and PP-Seq, on synthetic data. They demonstrate that their method is comparable in performance to PP-Seq under increasing background noise rate, while the performance of ConvNMF steadily drops. They then demonstrate their method on two experimentally-collected neural spike datasets, and present results indicating that their method infers the correct number and types of sequences, converge to similar parameter ranges in independent runs, and a constant expected tune cost with increasing number of observations.", "questions": "- How does the time complexity of this method compare to PP-Seq on a fixed-sized dataset (such as the songbird or rat datasets used)? In other words, what is the baseline time complexity cost imposed by the additions in our method (e.g. the non-parametric formulation)?\n- What is the dataset size at which using HDPP faster than PP-Seq?\n- Figure 5 shows the time cost of the HDPP method, which the authors imply should remain constant as a function of number of detected sequences. What was the number of detected sequences, as a function of the x-axis?\n- In Figure 5, why is there an early higher time cost (~50-100s) before settling in?", "limitations": "The authors do not mention any limitations of their method nor do they mention potential negative societal impact of their work. Please discuss in greater depth, for example, the tradeoffs that your method's non-parametric formulation and resulting inference algorithm may result in terms of complexity, uncertainty, or power. When, for example, would using PP-Seq be more desirable?", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n- Neural recordings for neuroscience are increasingly growing in size and length and under fewer experimental constraints. This direction of neuroscience research begets the need for methods that identify neural sequences in a streaming and non-parametric way. The authors' method would provide an important set of contributions to the field.\n- The authors' exposition of their model and inference method is clear.\n\n**Weaknesses**\n- The authors should improve the clarity of the conclusions that they draw from their results.\n- The authors validate their method against two existing methods, in particularly using PP-Seq to validate the number and type of sequences detected. I recommend that the authors expand the depth and rigor of their evaluations and their analysis of their method. For example, the authors do not demonstrate their method on a large dataset or provide evaluation of time and memory costs of their method vs. another method such as PP-Seq. I would also like to see their method perform on a dataset with a larger number of neural sequences, where there may greater uncertainty in sequence types.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "NfAQtdf4O8", "reviewer": "Reviewer_L7EJ", "summary": "One hypothesis about neural spike data is that it can be considered as a sequence of 'neural syllables' consisting of the spiking activity of a subset of neurons over a short period of time. Understanding these sequences would then enable relating activity recordings to behaviorally or experimentally relevant observables. The present manuscript proposes a method for unsupervised identification of such sequences.\n\nRecent ML literature, as cited in the manuscript, studied similar problems for point processes in different contexts. In that sense, this manuscript primarily represents an application of existing methodology on hierarchical inference in temporally structured data. Briefly, the manuscript proposes a particle filter based (sampling-based) solution to inferring sequence labels in a hierarchical model where the observables are samples from point processes. The problem is both important and relevant to this community.\n\nThe manuscript uses a Dirichlet process prior, which enables the method to decide on the number of sequence labels without relying on prior information. Indeed, such information is not easy to know in practice. Briefly, the sequence types (labels) are modeled as a Dirichlet process so that the same type can appear multiple types in a given recording. Neuronal spiking activity is then modeled as a Hawkes process conditioned on the sequence type. Overall, the model is complicated, but it is fitting to the underlying complicated problem.\n\nUpdate on Aug. 8: In response to the author rebuttal, I decided to increase my overall score from 5 to 6.", "questions": "I listed a few questions under Weaknesses above. I'd like to add a few more questions here:\n\n- Could Fig. 4 be turned into a comparative study as well? How much time would previous methods require to process that dataset? I'd be curious to see the results of other methods after temporal windowing as I mentioned under Weaknesses.\n\n- Could you please sort the neurons in Fig. 3 identically across the two compared methods to facilitate comparison?\n\n- Could you please discuss how the different methods would perform when the firing rates are lower?\n\n- Overall, the demonstrations use only a few sequence types. This may be in line with previous literature. However, one might expect to see a much larger set of sequence types in larger, longer recordings. Could you please discuss how the different methods would perform when the number of sequence types is larger?", "limitations": "The authors should discuss technical limitations of the work. That is, under which conditions can we expect it to fail? What are the roles of different noise sources, firing rates, etc?", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- Unsupervised, adaptive (streaming) inference of the number of sequence types\n- Computational scalability\n\nWeaknesses:\n- Poor presentation: The manuscript is full of typos and grammatical mistakes. While this obscures the underlying meaning very rarely, reading the manuscript becomes time-consuming and frustrating. Similarly, reasoning should be better and more precisely explained. For instance, the argument in lines 266-267 on using temporal windows to reduce computational load appears applicable to all methods. Please better explain why it would be more beneficial for the proposed method compared to existing methods.\n\n- Other than unsupervised inference of the number of types, one potential advantage of the proposed method could be real-time detection of sequences in a closed-loop experiment if inference can be made faster. (According to Fig. 5, it doesn't appear fast enough with the hardware used in that experiment.) However, this point was never discussed. Is this a desirable capability for neuroscience? What kind of desirable experiments could be performed by such a closed-loop setup? In my opinion, this point determines whether the proposed contribution is timely and impactful or a technical upgrade without practical consequences.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept