Overfitting Problem 2 Regularized Linear Regression 3 Regularized Logistic Regression 4 MLE and MAP Feng Li (SDU) Regularization and Bayesian Statistics September 20, 2023 2 / 25 Overfitting Problem Bayesian Statistics September 20, 2023 13 / 25 Maximum-a-Posteriori Estimation (MAP) Maximum-a-Posteriori Estimation (MAP): Maximize the posterior prob- ability of θ (i.e., probability in the light of θ)dθ The Bayes Rule lets us update our belief about θ in the light of observed data While doing MAP, we usually maximize the log of the posteriori prob- ability Feng Li (SDU) Regularization and Bayesian

of files：生成 mapTask 数量，一般是集群中（CPU 核数-1），我们测试虚 拟机就按照实际的物理内存-1 分配即可 ➢ Total MBytes processed：单个 map 处理的文件大小 ➢ Throughput mb/sec:单个 mapTak 的吞吐量 计算方式：处理的总文件大小/每一个 mapTask 写数据的时间累加 集群整体吞吐量：生成 mapTask 程序效率的瓶颈在于两点： 1）计算机性能 CPU、内存、磁盘、网络 2）I/O 操作优化 （1）数据倾斜 （2）Map 运行时间太长，导致 Reduce 等待过久 （3）小文件过多 8.2 MapReduce 常用调优参数 MapReduce优化（上） Map1方法 分区1 分区2 写入数据 第一次溢出 排序 第二次溢出 Combiner Combiner Shuffle的环形缓冲区大小，默认100m，可以提高到200m mapreduce.map.sort.spill.percent 环形缓冲区溢出的阈值，默认80% ，可以提高的90% 9）异常重试 mapreduce.map.maxattempts每个Map Task最大重试次数，一旦重试 次数超过该值，则认为Map Task运行失败，默认值：4。根据机器 性能适当提高。 1）自定义分区，减少数据倾斜;

Operator selectivity 6 • The number of output elements produced per number of input elements • a map operator has a selectivity of 1, i.e. it produces one output element for each input element it processes merge X merge A A X merge A1 merge A2 A2 A1 X X ??? Vasiliki Kalavri | Boston University 2020 map(String key, String value): // key: document name // value: document contents for each URL → list(v2) (k1, v1) → list(k2, v2) map() reduce() 25 ??? Vasiliki Kalavri | Boston University 2020 MapReduce combiners example: URL access frequency 26 map() reduce() GET /dumprequest HTTP/1

Keeping all that in mind, it is easy to see that floating-point xmin should map to 0, and xmax should map to 2b-1. How do we map the rest of the floating point values in between xmin and xmax to integer continuous values are also clamped to be in the range [xmin, xmax]. Solution: Note that we have to map all the values from [xmin, xmax] to 2b possible values (let’s call them bins). Figure 2-5 shows a visual is referred to as scale). Hence, [xmin, xmin + s) will map to the bin 0, [xmin + s, xmin + 2s) will map to bin 1, [xmin + 2s, xmin + 3s) will map to bin 2, and so on. Thus, to find which bin the given

log4j LoggingEvent. The log4j LoggingEvent is transformed as a Map containing the log details (level, logger name, message, …). This Map is sent to the appenders. The collector allows you to remotely the line into a typed Object (Long, Integer or String) before send it to the EventDispatcher data map. IDENTITY PARSER The identity parser doesn’t actually parse the line, it just passes through. It’s custom DecanterCamelEventExtender: public interface DecanterCamelEventExtender { void extend(Map decanterData, Exchange camelExchange); } You can inject your extender using setExtender(myExtender)

20 / 79 Transformations (2/4) ▶ map • Returns a new DStream by passing each element of the source DStream through a given function. ▶ flatMap • Similar to map, but each input item can be mapped to 21 / 79 Transformations (2/4) ▶ map • Returns a new DStream by passing each element of the source DStream through a given function. ▶ flatMap • Similar to map, but each input item can be mapped to 21 / 79 Transformations (2/4) ▶ map • Returns a new DStream by passing each element of the source DStream through a given function. ▶ flatMap • Similar to map, but each input item can be mapped to

Kalavri | Boston University 2020 Streaming word count textStream .flatMap {_.split("\\W+")} .map {(_, 1)} .keyBy(0) .sum(1) .print() “live and let live” “live” “and” “let” “live” (live nt
 val sensorData = env.addSource(new SensorSource)
 val maxTemp = sensorData
 .map(r => Reading(r.id,r.time,(r.temp-32)*(5.0/9.0)))
 .keyBy(_.id)
 .max("temp")
 maxTemp nt
 val sensorData = env.addSource(new SensorSource)
 val maxTemp = sensorData
 .map(r => Reading(r.id,r.time,(r.temp-32)*(5.0/9.0)))
 .keyBy(_.id)
 .max("temp")
 maxTemp

log4j LoggingEvent. The log4j LoggingEvent is transformed as a Map containing the log details (level, logger name, message, …). This Map is sent to the appenders. The collector allows you to remotely public interface DecanterCamelEventExtender { void extend(Map decanterData, Exchange camelExchange); } It’s very similar to the Decanter Camel "forwards" the data (collected by the collectors) to a JMS broker. The appender sends a JMS Map message to the broker. The Map message contains the harvested data. karaf@root()> feature:install decanter-appender-jdbc

获取正在消费队列列表 ProcessQueueTable 所有 MesssageQueue， 构建根据 broker 归类成 MessageQueue 集合 Map> 遍历 Map>的 brokername, 获取 broker 的 master 机器地址，将 brokerName 从 proccessqueue 获取批次消息， processqueue.takeMessags(batchSize) , 从 msgTreeMap 中移除消息放到临时 map 中 msgTreeMapTemp， 这个临时 map 用来回滚消息和 commit 消 息来实现事物消费 调回调接口消费消息，返回状态对象 ConsumeOrderlyStatus 根据消费状态，处理结果 ProcessQueue>的 keyset 的 messagequeue 去获取 RemoteBrokerOffsetStore.offsetTableMap 中的消费进 度， offsetTable 中 的 messagequeue 的 值 ， 在 update 的 时 候 如 果 没 有 对 应 的 Messagequeue 会构建， 但是也会 rebalance

cast(image, tf.uint8) return image, label train_ds = train_ds.map(resize_image) val_ds = val_ds.map(resize_image) test_ds = test_ds.map(resize_image) Note that the create_model() function here has two a Reduction cell. A normal cell's output feature map is identical to the input feature map. In contrast, a reduction cell reduces the output feature map to half. Figure 7-7 shows two child networks that primitive operations. The concatenation operation happens along the filter dimension to keep the feature map intact. Figure 7-9 shows the Normal and Reduction cells predicted by NASNet with the cifar10 dataset