My base model used wifi and beacon events to predict absolute position in a single timestamp. It used 50 events from 2 closest blocks of wifi events with hightest values of rssi and 10 closest beacon events. Events were sorted by rssi.
I trained one model on all sites. I used two bidirectional LSTMs - one on embeddings of wifi bssids + some numerical features related to each wifi event and one on embeddings of beacon_id + some numerical features related to each beacon event. Model also used embeddings of concatenated site and floor.
I think that the biggest improvement in this model was after I started interpolating waypoints in the training dataset. My best model was trained on waypoints interpolated every 1 second.
\nI also trained model, which predicted relative position of a smartphone based on sensor data. It predicted two numbers (deltaX, deltaY) based on 1 second of sensor data - 50 timestamps. I used Kalman Smoother to get targets for this model. It was a simple 1D-CNN model based on raw events.
\nPredictions from this model were interpolated, to approximate differences between positions in two consecutive waypoints. It achieved ~2.0 RMSE.
\nThe first step of my postprocessing was inspired by @saitodevel01's great notebook: indoor - Post-processing by Cost Minimization.
\nI assummed that models' predictions have the following distributions
\n$$(\\hat{X_i}, \\hat{Y_i}) | (X_i, Y_i) \\sim N_2((X_i, Y_i), \\sigma_1^2 I_2)$$
\nand
\n$$(\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) | (X_{i+1}, Y_{i+1}, X_i, Y_i) \\sim N_2( (X_{i+1}, Y_{i+1}) - (X_i, Y_i), \\sigma_2^2 I_2) $$
\nand all pairs \\( (X_i, Y_i) \\) are uniformly distributed in the corridor of the building, where
\\( (X_i, Y_i) \\) is a true position at timestamp \\( i \\) , \\( (\\hat{X_i}, \\hat{Y_i}) \\) is a prediction of absolute model, \\( (\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) \\) is a prediction of relative model and \\( \\sigma_1, \\sigma_2 \\) are RMSEs of absolute and relative models respectively.
\nAfter some math, it turns out that vector of \\( (X_1, Y_1, …, X_n, Y_n) \\) has truncated multivariate normal distribution with easy to calculate mean and covariance matrix. It is truncated in such a way, that each pair \\( (X_i, Y_i) \\) lies in the corridor of the building.
\nI implemented iterative method of sampling paths from this distribution similar to Gibbs sampling. In each iteration it samples pair \\( (X_i, Y_i) \\) using untruncated normal distribution conditioned on all the other pairs sampled so far until it samples a point inside the corridor or until it reaches given limit of trials. For each path I draw 500 samples and average last 200 samples.
\nThis method also allowed to use device id leak, by setting \\( \\sigma_1 \\) to some small value for leaked timestamps.
\nThis method without truncating to corridors had similar performance to Cost Minimiztion notebook - in fact I think they are almost equivalent. Adding map information improved my public LB score by ~0.3.
\nThe second step of my postprocessing was standard Snap to Grid, without any additional waypoints.
\n| method | \nprivate LB | \npublic LB | \n
|---|---|---|
| best absolute model | \n5.36934 | \n4.90242 | \n
| ensemble of 4 absolute models | \n5.30067 | \n4.88062 | \n
| above + device id leak + sampling postprocessing | \n3.33887 | \n3.00037 | \n
| above + snap to grid | \n3.07282 | \n2.64846 | \n
My base model used wifi and beacon events to predict absolute position in a single timestamp. It used 50 events from 2 closest blocks of wifi events with hightest values of rssi and 10 closest beacon events. Events were sorted by rssi.
I trained one model on all sites. I used two bidirectional LSTMs - one on embeddings of wifi bssids + some numerical features related to each wifi event and one on embeddings of beacon_id + some numerical features related to each beacon event. Model also used embeddings of concatenated site and floor.
I think that the biggest improvement in this model was after I started interpolating waypoints in the training dataset. My best model was trained on waypoints interpolated every 1 second.
\nI also trained model, which predicted relative position of a smartphone based on sensor data. It predicted two numbers (deltaX, deltaY) based on 1 second of sensor data - 50 timestamps. I used Kalman Smoother to get targets for this model. It was a simple 1D-CNN model based on raw events.
\nPredictions from this model were interpolated, to approximate differences between positions in two consecutive waypoints. It achieved ~2.0 RMSE.
\nThe first step of my postprocessing was inspired by @saitodevel01's great notebook: indoor - Post-processing by Cost Minimization.
\nI assummed that models' predictions have the following distributions
\n$$(\\hat{X_i}, \\hat{Y_i}) | (X_i, Y_i) \\sim N_2((X_i, Y_i), \\sigma_1^2 I_2)$$
\nand
\n$$(\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) | (X_{i+1}, Y_{i+1}, X_i, Y_i) \\sim N_2( (X_{i+1}, Y_{i+1}) - (X_i, Y_i), \\sigma_2^2 I_2) $$
\nand all pairs \\( (X_i, Y_i) \\) are uniformly distributed in the corridor of the building, where
\\( (X_i, Y_i) \\) is a true position at timestamp \\( i \\) , \\( (\\hat{X_i}, \\hat{Y_i}) \\) is a prediction of absolute model, \\( (\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) \\) is a prediction of relative model and \\( \\sigma_1, \\sigma_2 \\) are RMSEs of absolute and relative models respectively.
\nAfter some math, it turns out that vector of \\( (X_1, Y_1, …, X_n, Y_n) \\) has truncated multivariate normal distribution with easy to calculate mean and covariance matrix. It is truncated in such a way, that each pair \\( (X_i, Y_i) \\) lies in the corridor of the building.
\nI implemented iterative method of sampling paths from this distribution similar to Gibbs sampling. In each iteration it samples pair \\( (X_i, Y_i) \\) using untruncated normal distribution conditioned on all the other pairs sampled so far until it samples a point inside the corridor or until it reaches given limit of trials. For each path I draw 500 samples and average last 200 samples.
\nThis method also allowed to use device id leak, by setting \\( \\sigma_1 \\) to some small value for leaked timestamps.
\nThis method without truncating to corridors had similar performance to Cost Minimiztion notebook - in fact I think they are almost equivalent. Adding map information improved my public LB score by ~0.3.
\nThe second step of my postprocessing was standard Snap to Grid, without any additional waypoints.
\n| method | \nprivate LB | \npublic LB | \n
|---|---|---|
| best absolute model | \n5.36934 | \n4.90242 | \n
| ensemble of 4 absolute models | \n5.30067 | \n4.88062 | \n
| above + device id leak + sampling postprocessing | \n3.33887 | \n3.00037 | \n
| above + snap to grid | \n3.07282 | \n2.64846 | \n
Congrats! Great solution and solo gold.
", "rawMarkdown": "Congrats! Great solution and solo gold.", "votes": null } ], "comments": [ { "id": 1314113, "author_name": "robikscube", "author_url": "", "post_date": "05/19/2021 00:51:25", "content": "Congrats! Great solution and solo gold.
", "votes": null, "replies": [] } ], "raw_markdown_by_id": { "1313722": "# Absolute position model\n\nMy base model used wifi and beacon events to predict absolute position in a single timestamp. It used 50 events from 2 closest blocks of wifi events with hightest values of rssi and 10 closest beacon events. Events were sorted by `rssi`.\n\nI trained one model on all sites. I used two bidirectional LSTMs - one on embeddings of wifi bssids + some numerical features related to each wifi event and one on embeddings of beacon_id + some numerical features related to each beacon event. Model also used embeddings of concatenated `site` and `floor`.\n\nI think that the biggest improvement in this model was after I started interpolating waypoints in the training dataset. My best model was trained on waypoints interpolated every 1 second. \n\n# Relative position model\n\nI also trained model, which predicted relative position of a smartphone based on sensor data. It predicted two numbers (deltaX, deltaY) based on 1 second of sensor data - 50 timestamps. I used Kalman Smoother to get targets for this model. It was a simple 1D-CNN model based on raw events.\n\nPredictions from this model were interpolated, to approximate differences between positions in two consecutive waypoints. It achieved ~2.0 RMSE. \n\n# Postprocessing\n\nThe first step of my postprocessing was inspired by @saitodevel01's great notebook: [indoor - Post-processing by Cost Minimization](https://www.kaggle.com/saitodevel01/indoor-post-processing-by-cost-minimization). \n\nI assummed that models' predictions have the following distributions\n\n$$(\\hat{X_i}, \\hat{Y_i}) | (X_i, Y_i) \\sim N_2((X_i, Y_i), \\sigma_1^2 I_2)$$\nand\n$$(\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) | (X_{i+1}, Y_{i+1}, X_i, Y_i) \\sim N_2( (X_{i+1}, Y_{i+1}) - (X_i, Y_i), \\sigma_2^2 I_2) $$\nand all pairs \\\\( (X_i, Y_i) \\\\) are uniformly distributed in the corridor of the building, where\n\n\\\\( (X_i, Y_i) \\\\) is a true position at timestamp \\\\( i \\\\) , \\\\( (\\hat{X_i}, \\hat{Y_i}) \\\\) is a prediction of absolute model, \\\\( (\\hat{\\Delta X_i}, \\hat{\\Delta Y_i}) \\\\) is a prediction of relative model and \\\\( \\sigma_1, \\sigma_2 \\\\) are RMSEs of absolute and relative models respectively.\n\nAfter some math, it turns out that vector of \\\\( (X_1, Y_1, ..., X_n, Y_n) \\\\) has truncated multivariate normal distribution with easy to calculate mean and covariance matrix. It is truncated in such a way, that each pair \\\\( (X_i, Y_i) \\\\) lies in the corridor of the building.\n\nI implemented iterative method of sampling paths from this distribution similar to Gibbs sampling. In each iteration it samples pair \\\\( (X_i, Y_i) \\\\) using untruncated normal distribution conditioned on all the other pairs sampled so far until it samples a point inside the corridor or until it reaches given limit of trials. For each path I draw 500 samples and average last 200 samples. \n\nThis method also allowed to use device id leak, by setting \\\\( \\sigma_1 \\\\) to some small value for leaked timestamps.\n\nThis method without truncating to corridors had similar performance to Cost Minimiztion notebook - in fact I think they are almost equivalent. Adding map information improved my public LB score by ~0.3.\n\nThe second step of my postprocessing was standard Snap to Grid, without any additional waypoints.\n\n# Metrics\n\n| method | private LB | public LB |\n| --- | --- | --- |\n| best absolute model |5.36934 |4.90242 |\n| ensemble of 4 absolute models |5.30067 | 4.88062|\n| above + device id leak + sampling postprocessing |3.33887 | 3.00037|\n| above + snap to grid |3.07282 | 2.64846 |", "1314113": "Congrats! Great solution and solo gold." }, "source": "meta" }